a study on the profit-based quality-productivity

A STUDY ON THE PROFIT-BASED QUALITY-PRODUCTIVITY

RELATIONSHIP MODEL AND ITS VERIFICATION

IN MANUFACTURING INDUSTRIES

by

WEN-RUEY LEE, B.E., M.S.E.

A DISSERTATION

IN

INDUSTRIAL ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in

Partial Fulfillment of the Requirements for

the Degree of

DOCTOR OF PHILOSOPHY

Approved

Accepted

May, 1997

ACKNOWLEDGMENTS AKS-B^I

l\oy ly ^ I would like to express my sincere gratitude to Drs. Mario G. Beruvides,

James L. Smith, Jerry D. Ramsey, Hong-Chao Zhang, and Paul H. Randolph for

serving on my dissertation committee and for the guidance they have given me. I also

sincerely thank Dr. William J. Conover for his sage counsel and provision of related

software to this work.

I am especially indebted to my advisor. Dr. Mario G. Beruvides, for his

valuable suggestions, and patient guidance throughout my Ph.D. study. To me. Dr.

Beruvides is not only an excellent advisor but also a dear friend. Without his help, I

would not be who I am now.

Many others have contributed to this work throughout the years. Their

support is gratefully acknowledged. Especially, I would like to thank Mr. Chien K.

Lin, Mr. Yi T. Lin, Mr. Chin Y. Wu, Mr. Min H. Liao, Mr. Ming T. Chen, and Mr.

Meng C. Lin who assisted this research with great zeal in the data collection in the

field study.

I am grateful to my loving wife, Huei-Jen Homg, who gave me full support

during the days of studying at Texas Tech University. Finally, I would like to

dedicate this work to my father in commemoration of his passing away after my

dissertation defense.

11

TABLE OF CONTENTS

ACKNOWLEDGMENTS ii

LIST OF TABLES xii

LIST OF FIGURES xiv

CHAPTER

I. INTRODUCTION 1

1.1 Research Problem Statement 4

1.2 Scope of This Research 5

1.2.1 Research Question 6

1.2.2 Research Purpose 6

1.2.3 Research Objective 7

1.2.4 General Hypotheses 7

1.3 Limitations and Assumptions 8

1.3.1 Limitations 8

1.3.2 Assumptions 9

1.4 Relevance 9

1.4.1 Need for This Research 10

1.4.1.1 Theoretical Research Needs 10

1.4.1.2 Practical Research Needs 11

1.4.2 Benefits of This Research 11 1.5 Expected Results 12

111

2. LITERATURE REVIEW 13

2.1 Background 13

2.1.1 History 13

2.1.1.1 History of Quality 14

2.1.1.2 History of Productivity 16

2.1.1.3 Review of the Relationship between Quality and Profit 19

2.1.1.4 Review of the Relationship between Productivity and Profit 25

2.1.1.5 Review of the Relationship between Quality and Productivity 29

2.1.2 Definitions 36

2.1.2.1 Definitions of Productivity 37

2.1.2.2 Definitions of Quality 43

2.1.2.3 Definitions of Profitability and Profit 49

2.2 Current Profit-Based Quality, Productivity Models 53

2.2.1 Quality-Cost Model 53

2.2.1.1 Optimum Quality Cost Model 54

2.2.1.2 Dawes' Quality Cost Model 55

2.2.1.3 Poor-Quality Cost (PQC) Model 57

2.2.1.4 Taguchi's Quality Loss Function Model 59

2.2.2 Productivity-Profit Model 60

2.2.2.1 Adam-Hershauer-Ruch's Productivity-Profit Relationship Model 60

2.2.2.2 Papadimitriou's Profit Decomposition Model (PDM) 61

2.2.2.3 Sumanth's Productivity-Profit Relationship Model 64

iv

2.2.2.4 APC's Productivity-Profit Relationship Model 67

2.2.2.5 Miller's Productivity-Profit Relationship Model 67

2.2.2.6 Miller's Productivity-ROI Relationship Model 69

2.2.3 Quality-Productivity Relationship Models 71

2.2.3.1 Adam-Hershauer-Ruch Model 72

2.2.3.2 Deming's Model 73

2.2.3.3 Edosomwan's Model 73

2.2.3.4 Thor's Model 78

2.2.3.5 Sumanth's Quality-Profit-Productivity Relationship Model 80

2.3 Deficiencies and Limitations of Current Models 84

2.3.1 Deficiencies and Limitations of Quality-Profit Model 84

2.3.2 Deficiencies and Limitations of Productivity-Profit Model 87

2.3.3 Deficiencies and Limitations of Quality-Productivity Model 90

2.4 Research Agenda 95

2.4.1 Definitions of This Research 95

2.4.1.1 Definition of Quality 95

2.4.1.2 Definition of Productivity 96

2.4.1.3 Definition of Profit 98

2.4.1.4 Definition of Cost 98

2.4.2 Conceptual and Mathematical Models 100

2.4.2.1 Relationships among Quality, Price, Revenue, Volume Sold, and Costs 100

V

2.4.2.1.1 Price-Volume-Quality Relationship 100

2.4.2.1.2 Revenue-Quality Relationship 100

2.4.2.1.3 Cost-Volume-Quality Relationship 102

2.4.2.1.4 Cost-Quality Relationship 102

2.4.2.2 Quality-Profit Model 103

2.4.2.3 Productivity-Profit Model 105

2.4.2.4 Quality-Productivity Model 106

2.4.2.5 Conceptual Model of Linking Productivity and Quality in Confirmatory Study 108

2.4.2.6 The Comparison between the Proposed Model of This Research and Sumanth and Wardhanas' Model 109

2.4.2.7 Advantages of Relating Quality-Profit and Quality-Productivity

Models Based on Ranks 113

2.4.2.8 Contributions of This Research 114

3. RESEARCH METHODOLOGY 116

3.1 Research Process 116

3.2 Research Design 118

3.2.1 Type of Research 119

3.2.2 Research Focus 119

3.2.3 Research Hypotheses 120

3.2.4 Research Environment 123

3.2.4.1 ABC Company 123

3.2.4.2 XYZ Company 125

vi

3.2.5 Research Method 127

3.2.6 Research Instrument 127

3.2.7 Measurement of Costs and Profit 127

3.2.7.1 Measurement of Costs 129

3.2.7.2 Measurement of Profit 129

3.2.8 Test Plans of This Research 130

3.2.9 Specific Models Establishment 120

3.2.10 Unit of Analysis 135

3.2.10.1 ABC Company 135

3.2.10.2 XYZ Company 136

3.3 The Collection and Treatment of Data 136

3.3.1 Data Collection 137

3.3.2 Treatment of Data 137

3.4 Methodological Issues 140

3.4.1 Reliability 140

3.4.2 Validity 142

3.4.3 Replicability 144

3.4.4 Bias 145

3.4.5 Representativeness 147

3.5 Research Constraints 147

4. FIELD STUDY RESULTS, ANALYSIS, AND DISCUSSION 149

vu

4.1 Introduction 151

4.1.1 Company Contacts 151

4.1.2 Operation Definition 152

4.1.3 Primary Data Collected 154

4.1.4 Secondary Data Collected 154

4.2 Results of Collected Data 156

4.2.1 Production Cost Data 156

4.2.2 Revenue Data 158

4.2.3 Profit Data 160

4.2.4 Quality Data 162

4.2.5 Productivity Data 164

4.3 Data Analysis 166

4.3.1 Confirmatory Analysis 166

4.3.1.1 Method of Analysis 167

4.3.1.2 Quality-Profit Analysis 169

4.3.1.2.1 Spearman's Rho Test 169

4.3.1.2.2 Normality Test 171

4.3.1.2.3 Estimation of Confidence Interval of Correlation Coefficient 171

4.3.1.3 Productivity-Profit Analysis 172




viii

4.3.1.4 Quality-Productivity Analysis 175




4.3.2 Model Analysis 178

4.3.2.1 Method of Analysis 178

4.3.2.2 Quality-Profit Relationship Model Analysis 180

4.3.2.2.1 Specific Linear Regression Models 180

4.3.2.2.2 Residual Plots 181

4.3.2.2.2.1 Plots: Residuals Against r(Q) ~ Check the Linearity and Constant Variance 181

4.3.2.2.2.2 Plots: Residuals Against Time ~ Check the Nonindependence of Error Terms 184

4.3.2.2.2.3 Plots: Residuals Against Expected Values ~ Check the Normality of Error Terms 188

4.3.2.3 Productivity-Profit Relationship Model Analysis 190

4.3.2.4 Quality-Productivity Relationship Model Analysis 191

4.3.2.4.1 Specific Linear Regression Models 191

4.3.2.4.2 Residual Plots 192

4.3.2.4.2.1 Plots: Residuals Against r(Q) ~ Check the Linearity and Constant Variance 192

4.3.2.4.2.2 Plots: Residuals Against Time ~ Check the nonindependence of Error Terms 194

4.3.2.4.2.3 Plots: Residuals Against Expected Values ~ Check the Normality of Error Terms 197

IX

4.4 General Discussion 199

4.4.1 Discussion of Quality-Profit Relationship 199

4.4.2 Discussion of Productivity-Profit Relationship 200

4.4.3 Discussion of Quality-Productivity Relationship 202

4.4.4 Discussion of Data 204

5. CONCLUSIONS AND RECOMMENDATIONS 205

5.1 Summary 205

5.2 Further Discussion and Implications 208

5.2.1 Further Discussion 208

5.2.2 Implications 209

5.3 Conclusions 211

5.4 Recommendations 212

5.4.1 Theoretical Recommendations 212

5.4.2 Practical Recommendations 213

BIBLIOGRAPHY 214

APPENDIX

A: MATHEMATICAL MODELS DEVELOPMENT 234

B: QUALITY INSPECTION POINTS IN ABC AND XYZ COMPANIES 243

C. TABLE FOR THE SPEARMAN'S RHO TEST 246

D: RESULTS OF THE LILLEEFORS NORMALITY TESTS 248

E: A PROOF FOR THE RELATIONSHIP BETWEEN SLOPE OF A REGRESSION LINE BASED ON RANKS AND ITS CORRELATION 261

X

F: THE DURBIN-WATSON TEST PROCEDURE AND ITS TABLE 264

G: PREDICTED VALUES OF SPECIFIC MODELS OF QUALITY-PROFIT RELATIONSHIP 267

H: PREDICTED VALUES OF SPECIFIC MODELS OF QUALITY-PRODUCTIVITY RELATIONSHIP 271

XI

LIST OF TABLES

2.1 Definitions ofproductivity in the open literature 38

2.2 Definitions of quality in the open literature 44

2.3 Definitions of profitability and profit in the open literature 50

2.4 Comparison of QPR Values When Unit Reject Processing Cost Significantly Decreases 92

4.1 Definitions of Quality and Productivity in the ABC and XYZ Companies 153

4.2 Production Cost Data of Gingham in the ABC Company 157

4.3 Production Cost Data of Piece-dyed Fabric in the ABC Company 157

4.4 Production Cost Data of Token Ring in the XYZ Company 157

4.5 Production Cost Data of PNP Ethernet Combo in the XYZ Company 158

4.6 Revenue Data of Gingham in the ABC Company 158

4.7 Revenue Data of Piece-dyed Fabric in the ABC Company 159

4.8 Revenue Data of Token Ring in the XYZ Company 159

4.9 Revenue Data of PNP Ethernet Combo in the XYZ Company 159

4.10 Profit Data of Gingham in the ABC Company 160

4.11 Profit Data of Piece-dyed Fabric in the ABC Company 160

4.12 Profit Data of Token Ring in the XYZ Company 161

4.13 Profit Data of PNP Ethernet Combo in the XYZ Company 162

4.14 Quality Conformance Level of Gingham in the ABC Company 163

4.15 Quality Conformance Level of Piece-dyed Fabric in the ABC Company 163

Xll

4.16 Quality Conformance Level of Token Ring in the XYZ Company 163

4.17 Quality Conformance Level of PNP Ethernet Combo in the XYZ Company.. 164

4.18 Productivity Data of Gingham in the ABC Company 164

4.19 Productivity Data of Piece-dyed Fabric in the ABC Company 165

4.20 Productivity Data of Token Ring in the XYZ Company 165

4.21 Productivity Data of PNP Ethernet Combo in the XYZ Company 165

4.22 Summary of Spearman's Rho Test Results for Quality-Profit Relationship 170

4.23 Summary of Spearman's Rho Test Results for Productivity-Profit Relationship 173

4.24 Summary of Spearman's Rho Test Results for Quality-Productivity Relationship 176

4.25 Summary of the Estimated Linear Regression Models for Quality-Profit Relationship 181

4.26 The Durbin-Watson Test Results for the Quality-Profit Relationship of PNP and Token Ring Cases 187

4.27 Summary of the Estimated Linear Regression Models for Quality-Productivity Relationship 191

4.28 The Durbin-Watson Test Results for the Quality-Productivity Relationship of PNP and Token Ring Cases 196

5.1 Summary of Mathematical Models of This Research 207

B.l Quality Inspection Points in ABC and XYZ Companies 244

C. 1 Quantiles of the Spearman Test Statistic 247

F.l Durbin-Watson Test Bounds 266

G.l Predicted Values of Specific Models of Quality-Profit Relationship 268

H. 1 Predicted Values of Specific Models of Quality-Productivity Relationship 272

xiu

LIST OF FIGURES

2.1 Model for Optimum Quality Costs 54

2.2 New model for Optimum Quality Costs 55

2.3 Dawes'Quality-Cost Model 56

2.4 Effect of varying controllable PQC 58

2.5 Taguchi's Quality Loss Function 59

2.6 The Relationship between Profits and Input Costs 66

2.7 Chain Reaction Related to Quality and Productivity 73

2.8 A Framework for Understanding the Connection and Relationship between Productivity and Quality 74

2.9 Components of the PQMM 77

2.10 Process Quality and Productivity Are Essentially the Same 78

2.11 A Complete Productivity and Quality Measurement System 79

2.12 Costs of Non Quality and Quality Efforts as a Function of Quality of Conformance 82

2.13 The Relationships between Quality of Conformance, Profit, and Total Productivity 83

2.14 Cost-Profit Relationship 85

2.15 Price-Volume-Quality Relationship lOl

2.16 Revenue-Quality Relationship 101

2.17 Production Cost-Volume-Quality Relationship 102

2.18 Production Cost-Quality Relationship 103

XIV

2.19 Quality-Profit Relationship 105

2.20 Productivity-Profit Relationship 106

2.21 Quality-Productivity Relationship 107

2.22 Conceptual Model of Linking Quality and Productivity 109

3.1 Research Process of This Study 117

3.2 Main Hypotheses of This Research 121

3.3 Sub-Hypotheses of This Research 122

3.4 The Production Process of Gingham in the ABC Company 124

3.5 The Production Process of PNP Ethernet Combo in XYZ Company 126

3.6 Research Method in the Field Study 128

3.7 Test Plan for Quality-Profit Relationship 131

3.8 Test Plan for Productivity-Profit Relationship 132

3.9 Test Plan for Quality-Productivity Relationship 133

3.10 Data Collection Form 138

4.1 Research Sequence of Chapter 4 150

4.2 Residual Plots: Residuals Against Ranks of Quality 182

4.3 Residual Time Plots: Residuals Against Time Series 185

4.4 Residual Plots: Residuals Against Expected Value 189

4.5 Residual Plots: Residuals Against Ranks of Quality 192

4.6 Residual Time Plots: Residuals Against Time Series 194

4.7 Residual Plots: Residuals Against Expected Value 197

XV

D. I Normality Test for Quality-Profit Data of Gingham (Factory A, ABC Company) 249

D.2 Normality Test for Quality-Profit Data of Gingham (Factory B, ABC Company) 249

D.3 Normality Test for Quality-Profit Data of Gingham (Factory C, ABC Company) 250

D.4 Normality Test for Quality-Profit Data of Piece-dyed Fabric (Factory A, ABC Company) 250

D.5 Normality Test for Quality-Profit Data of Piece-dyed Fabric (Factory B, ABC Company) 251

D.6 Normality Test for Quality-Profit Data of Piece-dyed Fabric (Factory C, ABC Company) 251

D.7 Normality Test for Quality-Profit Data of PNP Ethernet Combo 252

D.8 Normality Test for Quality-Profit Data of Token Ring 252

D.9 Normality Test for Productivity-Profit Data of Gingham (Factory A, ABC Company) 253

D. 10 Normality Test for Productivity-Profit Data of Gingham (Factory B, ABC Company) 253

D. 11 Normality Test for Productivity-Profit Data of Gingham (Factory C, ABC Company) 254

D. 12 Normality Test for Productivity-Profit Data of Piece-dyed Fabric (Factory A, ABC Company) 254

D.13 Normality Test for Productivity-Profit Data of Piece-dyed Fabric (Factory B, ABC Company) 255

D. 14 Normality Test for Productivity-Profit Data of Piece-dyed Fabric (Factory C, ABC Company) 255

D. 15 Normality Test for Productivity-Profit Data of PNP Ethernet Combo 256

D. 16 Normality Test for Productivity-Profit Data of Token Ring 256

XVI

D. 17 Normality Test for Quality-Productivity Data of Gingham (Factory A, ABC Company) 257

D. 18 Normality Test for Quality-Productivity Data of Gingham (Factory B, ABC Company) 257

D. 19 Normality Test for Quality-Productivity Data of Gingham (Factory C, ABC Company) 258

D.20 Normality Test for Quality-Productivity Data of Piece-dyed Fabric (Factory A, ABC Company) 258

D.21 Normality Test for Quality-Productivity Data of Piece-dyed Fabric (Factory B, ABC Company) 259

D.22 Normality Test for Quality-Productivity Data of Piece-dyed Fabric (Factory

C, ABC Company) 259

D.23 Normality Test for Quality-Productivity Data of PNP Ethernet Combo 260

D.24 Normality Test for Quality-Productivity Data of Token Ring 260

xvii

CHAPTER I

INTRODUCTION

For years quality and productivity have been regarded as two important

indexes of company performance. Many companies hope to pursue high quality and

high productivity at the same time. However, in most cases, these two variables are

not linked together in the production system mainly because of the variety of their

definitions (Human Resources Productivity, 1983; Garvin, 1988; Belcher, 1987;

Hoffherr & Moran & Nadler, 1994; Smith, 1990). Additionally, these two variables

are not taken into account together because: (1) the objectives of quality management

and productivity management are viewed as contradictory,^ (2) the definitions of

quality and productivity are difficult to define, (3) the affecting factors on quality or

productivity are too numerous, (4) seemingly, quality and profit have no direct

connection,^ and (5) many companies believe that they have distinct characteristics

which may not be subject to any model.

' Deming (1986), Belcher (1987), Darts (1990), Hart and Hart (1989), Kaydos (1991), and Omachonu and Ross (1994) also have noted this misconception in their research.

^ Pirsig (1974) believes quality cannot be defined. McNealy (1993) states that quality is as hard as "art" to define. Mohanty and Yadav (1994) also claim that quality is a difficult concept to define. Deming (1986) maintains that quality is defined by management. Kendrick (1984) asserts that productivity cannot be measured directly. Yet others, such as Smith (1986), Kaydos (1991), Price (1990), regard quality and productivity as the same thing.

^ Sumanth and Wardhana (1993) point that some companies do not believe "quality and profit go hand in hand," (p. 463)

The first reason, stated above, was especially prevalent in the past. Deming

(1986) asserts that this erroneous concept of quality and productivity management

contradiction is common in American industries; therefore, he firmly asserted that

improving quality will result in improved productivity. He believed the relationship

between quality and productivity is strongly positive. However, he interpreted this

relationship by reasoning, that is, Deming presented no mathematical model to

backup his assertion. Managers believe his assertion is correct because the logic is

reasonable.

The second reason that quality and productivity are difficult to define, lies in

the debatable definitions. So far the well-known definitions of quality are too

abstract to relate to productivity. On the other hand, productivity has different levels

(or units of analysis) and types.' Each level or type ofproductivity has different units

of measure. The type or unit of measure for productivity which should be used to

relate to quality is debatable.

The third reason, that the affecting factors on quality or productivity are too

numerous, illustrates the difficulties of relating quality and productivity. Generally,

the current quality-productivity relationship models can be classified into two

categories: qualitative models and quantitative models. The qualitative models

outnumber the quantitative models because the latter need measurable variables. A

'* Sumanth (1979) deals with productivity at four levels: International, National, Industry, Company. Sumanth (1994) classifies productivity into three types: Total Productivity, Total Factor Productivity, and Partial Productivity. Kendrick (1984) deals with productivity at another four levels: National, Industrial, Company, and Personal.

qualitative model is easier to understand, but has less applicability compared with a

quantitative model. However, because many factors are not easy to measure,

quantitative models have limitations in application. Therefore, companies may not

believe it is practical to link quality and productivity.

The fourth reason, that quality and profit have no direct connection, illustrates

that current models cannot reflect the impact on profit. Profit is the main concern of

management, ff a quality-productivity model cannot estimate the impact on profit, it

loses its attractiveness to the management. However, because quality is an abstract

concept, it is hard to directly link quality and profit together. Although productivity

can be measured in terms of profit, it is not common to quantitatively relate quality to

profit. Therefore, a quality-productivity model without profit as a base may not be

attractive to industries.

The last reason, that each company believes it has its own characteristics

which may not be subject to any model, illustrates their perception that their

production features are different from others. They believe that a model may be

applicable to others, but not to them. Each company has its own production features;

however, a generic model can be tailored to the user's own purpose. Most models

found in open literature are not originally developed for a specific company. Hence,

the notion that it is impractical to link quality and productivity for use is incorrect.

These five reasons leave the following questions unanswered: High quality

and high productivity are all pursued by companies, but how can they be related to

each other? Is this potential relationship model meaningful for companies? How can

the relationship be applied in practice? This study will answer all these questions.

This research focuses on the profit-based quality-productivity relationship

model and its verification in manufacturing industries. In this chapter, the problem

statement is presented in section 1.1. The scope of this research, including the

research question, purpose and objective, are addressed in section 1.2. The

limitations and assumptions of this research are presented in section 1.3. In section

1.4, needs and benefits of this research are explained. Finally, section 1.5 presents

the expected results.

1.1 Research Problem Statement

Quality and productivity are two measures of interest in most every company.

Their relationship is also a concern of management. From the open literature, it is

understood that productivity will increase as product quality increases (Shetty &

Buehler, 1985; Hayes, 1985; Deming, 1986; Hart & Hart, 1989; Darts, 1990; Kaydos,

1991; Tribus, 1992; Barrett, 1994; Omachonu & Ross, 1994). However, fewer

quality-productivity relationship models are expressed in a mathematical way. A

mathematical model of the quality-productivity relationship provides more clear

information for parameter control than does a descriptive model. Therefore, an

appropriate mathematical model relating quality and productivity is sought to meet

the needs of management.

Since multiple units of measure are used in quality as well as productivity

measures, a common measurement unit must be set in order to relate quality and

productivity. Perhaps a better common unit of measure in this quality-productivity

relationship is profit, since profit is most attractive to management. Hence, a study on

the profit-based quality-productivity relationship model is conducted in this research.

Finally, the applicability of the developed quality-productivity relationship

model must be discussed. A study on the verification of this proposed model in

Taiwan's manufacturing industries is surveyed. Taiwan's manufacturing industries

are chosen for the follovWng reasons: (1) Taiwan is a typical Newly Industrialized

State (NIS). The government adopts an export-oriented trading policy. This policy

encourages all enterprises to emphasize quality and productivity, (2) Many managers

in Taiwan's manufacturing industries possess common knowledge of quality control

and productivity management. This is especially helpful in communication when

conducting this research, (3) Information on Taiwan's manufacturing industries is

readily available for this research.

1.2 Scope of This Research

This section addresses the research question in which this study is interested.

The research purpose and objective are also included in this section to help direct the

efforts of this research.

1.2.1 Research Question

The main questions this work will address are as follows:

1. What is the quality-productivity relationship model based on profit?

2. Is the profit-based quality-productivity relationship model applicable in

manufacturing environment?

To answer the two main questions, it is necessary to understand further:

a. What is the quality-profit relationship?

b. What is the productivity-profit relationship?

c. How many quality-productivity relationship models are currently

available? Are they generic or specific? Do they need to be revised or

modified for this research?

1.2.2 Research Purpose

This research will attempt to provide an applicable profit-based quality-

productivity relationship model for manufacturing industries. This model will

convince the management of that quality and productivity are positively related, and

the enhancement of either quality or productivity will increase profit. An additional

purpose of this research is to show whether the developed quality-productivity

relationship model is applicable to an individual company. It is expected that the

developed model is not only theoretically sound, but also may be practically used by

companies in the real world.

1.2.3 Research Objective

This research has two main objectives: (1) develop a mathematical quality-

productivity relationship model based on profit, and (2) Investigate the applicability

of this model in the manufacturing industries.

In achieving these objectives, the following secondary objectives are included:

1. To review the existing models related to the quality-productivity

relationship.

2. To explore the relationship between quality and profit.

3. To explore the relationship between productivity and profit.

4. To conduct an empirical study in Taiwan in order to confirm the

developed model.

1.2.4 General Hypotheses

The general hypotheses regarding this research are:

1. Quality and profit are related, and a model may illustrate the relationship

between these variables.

2. Productivity and profit are positively related, and there is a model to relate

these two variables.

3. Quality and productivity are related, and a model may illustrate the

relationship between these variables.

1.3 Limitations and Assumptions

In this research, some determination of the limitations and assumptions is

required. These limitations and assumptions are helpftil in focusing this research. If

the model proposed in this research is tailored for a specific purpose, the limitations

or assumptions will possibly change.

1.3.1 Limitations

The limitations of this research are:

1. This research deals only with manufacturing companies. Service

organizations will not be included in the scope of this research.

2. The intangible factors of quality and productivity are not discussed in this

research.

3. The relationship between quality and productivity is linked based on profit.

4. The productivity measure (unit of analysis) used in this research is limited

to the company level. The productivity measures of national, industrial,

and individual levels are not considered in this study.

5. The productivity type used in relating productivity to quality is restricted to

the Total Productivity Model.

6. The study on the applicability of proposed model is conducted in Taiwan's

manufacturing organizations.

8

7 This research considers all issues within this research from an industrial

engineering perspective. Implications concerning other disciplines are not

addressed in depth.

1.3.2 Assumptions

The assumptions of this research are:

1. The manufacturing company is a profit-oriented company.

2. The company has the intention and capability of improving its quality and

productivity.

3. Quality can be linked wdth profit.

4. Productivity can be measured in terms of profit.

5. In general, the issues considered are applicable to manufacturing

companies.

6. Except where specified, all terms used in this research reflect the common

usage as found in the quality and productivity literature.

1.4 Relevance

This section describes the needs and benefits of this research. The needs of

this research provide the motive required for carrying out the research. Benefits of

this research are followed by the results of this study.

1.4.1 Need for This Research

This research deals with the theoretical relationships between quality,

productivity, and profit. A confirmatory study on the theoretical model is also

conducted to verify model's applicability. The specific theoretical and practical

research needs will be discussed in the following two subsections (1.4.1.1 and

1.4.1.2) respectively.

1.4.11 Theoretical Research Needs

Managers seek to improve quality by every possible means. They all

understand the importance of quality. However, the problem of how profit is affected

by quality is not easy to measure. In general, the relationship between quality and

profit is easier to explain in the descriptive approach; however, it lacks precision.

Perhaps a better way to realize how the quality level affects profit is to establish a

mathematical relationship model between these two variables. Through this

mathematical model, the optimal quality level in which the profit is maximum can be

identified.

The needs for research on the relationship between productivity and profit are

identical to those for quality and profit. The basic definition ofproductivity is a ratio

of output to input; therefore, if the output is measured in tenns of profit, it is easier to

quantitatively estimate the relationship between productivity and profit. However, it

10

is not easy to measure the relationship between productivity and profit without a

definite model. This research intends to determine such a mathematical model.

In addition, because productivity is strongly affected by quality, managers are

interested in their relationship. By establishing a Quality-Productivity relationship

model based on profit, it would help the managers and researchers realize more

firmly that profit can be increased by enhancing quality or productivity.

1.4.1.2 Practical Research Needs

This research is also interested in understanding the applicability of the

proposed model in manufacturing companies. Any model will undoubtedly be

accepted if it can be proved or confirmed. In general, management in industry is

more interested in the model's applicability than in the model's theory. Taiwan, as a

newly industrialized nation, has the desire to practically understand the relationships

between quality, productivity, and profit. This need is also a driving force of this

study.

1.4.2 Benefits of This Research

The benefits of this research are as follows:

1. Present an updated literature review on the quality-profit, productivity-

profit, and quality-productivity relationships.

11

2. Determine the relationship between quality and productivity from the profit

point of view.

3. Develop a relationship model of the quality and productivity that can be

analyzed and evaluated for the purpose of management.

4. Present a theoretical, quantitative research approach for measuring the

relationship between quality and productivity.

5. Confirm the proposed relationship model of quality and productivity

through field study.

1.5 Expected Results

This research should result in the following: (1) A mathematical model of the

quality-productivity relationship is to be set up fi-om the profit viewpoint. (2) The

applicability of the proposed model to manufacturing companies could be

investigated and verified. (3) The established specific model could be used as a

predictor for manufacturers. In addition to these three results, all of the relationship

models related to quality-profit, productivity-profit, and quality-productivity are to be

examined, analyzed, and classified through the literature review. Conclusions and

recommendations related to the findings of this research are also to be provided.

12

CHAPTER 2

LITERATURE REVIEW

2.1 Background

The quality-productivity relationship is linked by the measures of quality and

productivity. Because of the variety of quality and productivity measures, it is

necessary to base these two variables on a common unit of measure. Profit is

selected as this base because it relates to both quality and productivity. Besides,

profit is the most critical issue for management. In addition, to understand the basic

definitions and history of quality and productivity, it is also necessary to review the

relationships between quality, productivity, and profit. Therefore, in this section, the

history of quality and productivity are first briefly introduced. The relationships

between quality, profit, and productivity found in the open literature are then

presented. Various definitions of quality, productivity, and profitability are also

examined in this section.

2.1.1 History

History provides experiences and learning to deal with the future. It is helpful

to examine the history of quality and productivity before exploring the relationship

between the two variables. In addition to examining the history of quality and

productivity, these subsections illustrate the relationships between quality and profit.

13

productivity and profit, and quality and productivity. In order to more thoroughly

understand the quality-productivity relationship, review of this relationship is not

limited to profit-based.

2.1.1.1 History of Oualitv

The concept of quality has existed for a long time. According to Duncan

(1974), "Quality control is as old as industry itself (p. 1). Shewhart (1939) points out

more definitely that the inspection standard of a "go" tolerance limit appeared in

1840. About 30 years later, the improved concept of "go, no-go" tolerance limits

was developed. However, the management of quality, regarded as a professional

task, can be traced back to F. W. Taylor (1911). Known as the father of scientific

management, Taylor was the first to regard management and production as different

functions. In 1931, W. A. Shewhart (1931) introduced statistical quality control in

his book "Economic Control of Quality of Manufactured Product." In 1941, W. E.

Deming began to teach quality-control techniques in the U. S. War Department. He

later taught statistical quality control in Japan in 1950. To thank Deming for his

contribution, the Japanese established the Deming Prize in 1951. Another master in

quality control, J. M. Juran also gave seminars to the Japanese beginning in 1954.

^ In his book "The principles of scientific management," Taylor presented four principles for management. The fourth was "an almost equal division of the work and the responsibility between the management and the workmen," (p. 37). He indicated that nearly one-half of the production problem was up to the management. Therefore, he asserted that management was a professional task which should be separated fi-om the worker's job. According to Taylor's assertion, the management of quality should also be viewed as an independent function fi-om the worker's job.

14

This was "a turning point m emphasizing quality control for management" (Hosotani,

1992, p. 4).

It was not until the introduction of the concept of reliability that quality was

seldom measured relating to a product's life-time. Reliability engineering was

originated and conducted by the Advisory Group on Reliability of Electronic

Equipment (AGREE), formed in 1952, for studying and analyzing the failures of

electronic military equipment. The 1957 AGREE report formally defined the term

reliability and "formed the basis for modem methods and procedures" (Evans &

Lindsay, 1989, p. 255). In 1961, Martin Company developed the Zero Defects

Program and achieved zero defects in the American Army's Pershing missile system.

This Zero Defects concept was later introduced by J. F. Halpin, Director of Quality of

the Martin Company, in 1966. In the year of 1961, A. V. Feigenbaum first presented

the concept of Total Quality Control. K. Ishikawa introduced Quality Control Circles

in the following year. Mitsubishi's Kobe Shipyard in Japan first used Quality

Function Deployment (QFD) in 1972. The QFD technique was introduced to the U.

S. in 1983 by Professor Y. Akao of the University of Tamagawa. G. Taguchi, a

Japanese engineer, introduced a new approach in the early 1980s. His approach,

which later became known as the Taguchi Method, was used to design products and

reduce loss through what he termed the "Loss Function."

People are a very important factor to the quality. Research and

implementation related to the quality of work life (QWL) began to be emphasized.

15

According to Riggs and Felix (1983), the development of QWL can be traced to the

eariy 1970s. However, "Major efforts to make QWL an emerging fact in the

employees' work life have been under way since the 1980 National Memorandum of

Understanding was issued" (Shetty & Buehler, 1985, p. 135). Because of the risk

assumption, Shingo (1986) believes that traditional statistical methods cannot achieve

the zero defects level. In order to prevent and eliminate all possible defects, he then

proposed a mistake-proof system, called the poka-yoke system, and a source

inspection system. In 1987, the International Organization for Standardization (ISO)

published the ISO 9000 series to serve as the international standards of quality.

These standards were revised in 1994, and gradually have became more prevalent

since their adoption by many countries, especially the European Community nations.

The ISO 9000 series has become the supreme standards governing quality aspects.

Since the quality-productivity relationship is the key issue of this research, it

is also essential to understand the history ofproductivity. We will make a brief

introduction to its history in the following.

2.1.1.2 Historv of Productivity

According to Sumanth (1994), "probably, the first time the word 'productivity'

was mentioned was in an article by Quesnay in the year 1766" (p. 3). A more

detailed review ofproductivity is made by Kendrick (1977). In his book

Understanding Productivity, Kendrick mentioned that "the early estimates of

16

productivity were in terms of output per unit of labor input," (p. 19). This concept

was used by the eariy economists (e.g., Adam Smith in 1776) in the labor theory of

production and value (Kendrick, 1977). Kendrick recounted that in the latter

nineteenth century, Alfred Marshall advocated that man-made capital goods, labor,

and land were the basic factors of production. Marshall's recognition of the basic

factors of production became "the basis for the concepts of production function and

productivity" (Kendrick, 1977, p. 20).

The first estimates ofproductivity, in terms of output-per-hour, were

presented by the United States Bureau of Labor in the mid-1880s (Kendrick, 1977).

C. D. Wright, the first commissioner of labor in the U.S., published a report called

"Hand and Machine Labor," in 1898. According to Adam and Dogramaci (1981),

Wright's report, which studied company productivity and costs, is a remarkable

landmark in the history ofproductivity. Sumanth (1979) pointed out that probably the

first productivity index, a ratio of output to the number of wage earners, was

presented by F. C. Mills in 1899. Taylor (1911) in his renowned book The Principles

of Scientific Management, provided some examples for describing how the increase

in human productivity can be reached by applying the principles and methods of

scientific management. In addition, his work measurement is an effective tool for

improving labor productivity.

After the Great Depression of the 1930s, productivity estimates and analyses

were revived (Kendrick, 1977). During this period, the Bureau of the Census "began

17

publication of industry summaries on value added per man-hour" (Adam &

Dogramaci, 1981, p. 13). Since 1940, the Bureau of Labor Statistics (BLS)

investigated productivity performance in certain industries and published the first

regular government estimates ofproductivity. Today the BLS still "is the major

source of industrially based data on labor productivity" (Smith, 1990, p. xiii). The

initial development of the total factor productivity approach began after World War

II. According to Kendrick, productivity studies in the U. S. and abroad interacted

with the movement in many countries, beginning about 1950. The European

Productivity Agency, which became known as the European Association of National

Productivity Centers, was set up after 1952 to integrate the activities of the

international centers (Kendrick, 1977). Japan began its productivity movement in

1953. Two years later, the Japan Productivity Center began operation. The Asian

Productivity Organization, which is located in Tokyo, was established from the Japan

Productivity Center in 1961. No productivity agency was set up in the U. S. before

1970.

Due to "the failure to tax-finance the Vietnam escalation" and "the energy-

price revolution," inflation was actuated firom the mid-1960s to the early 1970s. This

inflation stimulated and reinforced the increased rate of improvement ofproductivity

in organizations (Adam & Dogramaci, 1981, p. 13). Also in the 1970s, the BLS

executed a large-scale measurement program to measure the employee's productivity

in federal organizations. In July 1970 the National Commission on Productivity was

18

created and its name was then changed to the National Center for Productivity and

Quality of Working Life in June, 1974 (Sumanth, 1994). In 1975, the U.S.

Department of Commerce began holding seminars to educate the company managers

in methods ofproductivity measurement (Adam & Dogramaci, 1981). In 1980, the

U. S. Senate first declared October 6-12 as the National Productivity Improvement

Week (Sumanth, 1994).

After briefly reviewing the histories of quality and productivity respectively,

the relationships between quality, productivity, and profit v^ll be subsequently

reviewed. In general, profit is the difference between total revenues and total costs,

while profitability is the ratio of total revenues to total costs. Theoretically, profit

and profitability have different definitions. However, unless otherwise specified in a

model or quoted materials, profit and profitability are considered interchangeable

terms when comparing quality and productivity in the following subsections. After

the relationship between quality and profit is examined, the relationship between

productivity and profit will be investigated,. Finally, the quality-productivity

relationship will be addressed.

2.1.1.3 Review of the Relationship between Quality and Profit

The relationship between quality and profit is inseparable. "Seeking profit by

making quality a priority" (Hosotani, 1984, p.23), and "Quality is the input,...

Profits, ROI,... are results" (Bhote, 1991, pp. 10-11) illustrate the remarkable

19

relationship between quality and profit. Some even regard quality as a synonym of

profitability. Undoubtedly, managers believe that better quality results in more

profit. However, on the surface, quality does not directly relate to profit. From the

quality viewpoints, the increase of profit is due to the following two approaches.

First, the cost decreases while the selling price and volume either remain the same or

increase. Second, the increase of purchasers leads to increased profit. Nevertheless,

these two ways are strongly cross-related.

The first approach is cost-driven, meaning that more profit is made because

the cost is reduced first. Weinberg (1969) believes that optimum quality, not highest

quality, means lower costs and is the most economic way to make profit. Crosby

(1979) emphasizes the inverse relationship between conformance quality and costs.

Therefore, he asserts that "Quality is Free," and places it as the title of his book. He

also indicates that as quality improves, costs reduce, and hence resulting in more

profits. John Heldt, an experienced consultant in implementing quality cost system,

states that "Reducing the cost of poor quality will increase your overall profit more

than doubling sales" (Harrington, 1987, p. 157). Duncan and Bowen (1984)

introduce an Integrated Metrology System to boost product quality for profit

improvement by reducing the cost of quality. Williams (1984) believes that the gross

profit of a company is enhanced by the improvement of quality and productivity, and

^ Ray Witt, a former president of American Foundrymen's Society, in a speech encouraged the foundrymen to emphasize quality. He stated that, "Quality and profitability are synonymous terms in the metalcasting industry." (From "Proactive Quality Control Is the Key to Profitability in the 1990s").

20

the reduction of cost. As quality improves, cost reduces and profit increases. Katzan

(1985) mentions that poor quality is costly and has a ripple effect, which it will eat

away profits. Lester, Enrick, and Mottley (1985) describe how lower quality cost,

through the reduction of scraps, reworks, inspections, etc., results in higher return on

investment, an index of profitability. Day (1988) demonstrates how profits can

double because of the elimination of scrap and rework through the improvement of

process capability. Price (1990) also points out that high quality, through quality cost

reduction, results in high profit.

The most impressive assertion regarding the cost-driven approach of the

quality and profit relationship is proposed by G. Taguchi. In the early 1980s, Taguchi

presents a "loss fimction" concept, which aims at reducing the variability of products.

The variability is product's deviation fi-om its target value. He believes that the loss

caused by the variability is incurred by society. Therefore, Taguchi (1985) defines

quality as the loss a product imposes on society after this product is shipped. He

maintains that variability must be decreased so that the total loss can be reduced.

Because of the reduction of loss, profits increase. Since the increased profit can be

quickly obtained fi-om the reduction of costs, Taguchi's method has been widely

applied in industries.

The second approach is market-driven, which emphasizes that profit is

increased by more customers. Halpin (1966) stresses that Zero Defects can deliver

the best possible product at the lowest possible price on time. This will "assure

21

management a strong market position in the years to come" (p. 186). In another

book, Crosby (1984) stresses that if the top management respected the rights of

customers like it respects the rights of the stockholders, then quality and profit will

both increase at the same time. Tuttle (1985) introduces an ACE (Acquisition and

analysis of Customer Experience) system believed to improve quality and profit.

This system mainly emphasizes customer response and takes advantage of customer

feedback to improve quality and profit. Buzzell and Bradley (1987) assert that with

higher quality, stronger customer loyalty and more repeat purchases can result. Owen

(1989) believes that attaining higher quality will cost more at first; however, this cost

will pay off and result in a higher return on investment. Ishikawa (1990) stresses his

quality assurance approach is "customer-first philosophy," which ensure that a

company is successful in market. Smith (1990) points out that quality is a strategic

and competitive weapon. With a higher level of quality, it is easier to attract

customers and increase sales. Bauer (1990), a retired director of IBM and winner of

National Quality Award in 1990, points out that "Market-Driven Quality" is IBM's

quality strategy, and aims at enlarging market shares. Both Huge (1990) and Bhote

(1991) indicate that PIMS(Profit Impact of Market Strategy) research shows a strong

relationship exists between quality and profitability. Huge also indicates more

definitely that if the quality improves fi-om low to high, market share and profit on

sales will at least double fi^om low to high. Tschohl and Franzmeier (1991) claims

that profit is determined by customer satisfaction. Although good product quality

22

alone will not guarantee profit, it helps to increase customer satisfaction and profit.

Munoz, Civille, and Carr (1992) think a strong relationship exists between quality

and customers' buying decisions. Customers not only care about quality, but also buy

quality. Munoz et al. believe this is the reason that Japanese businesses succeed in

U.S. markets. Oakland (1993) thinks quality is the most important factor that

determines an organization the reputation and hence results in maximum profit.

Research which simultaneously focuses on cost and customer is abundant.

Deming (1982) indicates that improved quality means costs and prices decrease,

making the company more competitive in market. Bravemman (1983) thinks an

appropriate quality assurance system can not only reduce waste, but can also attract

customer will. This an important issue in maximizing profits. Sink (1985) defines

profitability as a ratio of total revenues to total costs. Either increasing revenues or

reducing costs can produce higher profits. Feigenbaum (1986) maintains that quality

is the "most powerful corporate leverage point for achieving both customer

satisfaction and low costs" (p. 27). This means that more profit can result from

improving quality and reducing cost simultaneously. Evans and Lindsay (1989)

believe that "Better quality of design will eventually lead to better market share and

increased profits" (p. 43). They also think that quality cost analysis is a valuable tool

in increasing profitability. To maximize profit, Perigord (1990) suggests an

optimized Q/P (Quality/Price) ratio for reducing internal cost and increasing client

satisfaction. Christopher (1993) regards profitability as the interaction between costs

23

and revenues. Juran and Gryna (1993) explain the four reasons high quality produces

more profits: by the increase of market share, by earning premium prices, by

obtaining benefits of a larger production scale, and by attracting and sticking to

customer's loyalty. Omachonu and Ross (1994) describe the relationship between

quality and profit. They believe that good quality can reduce costs while

simultaneously improving market share and hence profit. According to Eureka and

Ryan (1995), Taguchi indicates that quality improvement is the most effective way to

reduce cost and increase sales at the same time.

Although all the research stated above agree that better quality will produce

more profit, this agreement implies an important assumption: the product

manufactured must have market value. Without this assumption, a quality product

may not result in profit. For example, a company was still producing slide rules after

the advent of the calculator, no matter how well the product quality resulted, it is

obvious that this product would not produce profit to the manufacturer. This product

may have zero defects, have minimal costs, but have no market value in the age of

calculators. Market influence can reverse the positive relationship between quality

and profit. Therefore, quality does not in and by itself imply profitability.

From the above review of the relationship between quality and profit, it is

significant to note that there is no mathematical model directly relating quality and

profit. Although most research concludes that quality and profit have a close

relationship, no theoretical research can prove the relationship. By surveying (e.g..

24

PIMS), this relationship could be confirmed. However, quantitatively examining the

relationship between quality and profit from cost or productivity viewpoints has been

studied (Juran & Gryna, 1970; Harmon, 1984; Taguchi, 1986; Dawes, 1987;

Harington, 1987; Day, 1988; Arora & Sumanth, 1992; Sumanth & Wardhana, 1993).

Therefore, it can be implied that the exploration for the quality-profit relationship

model is more likely through intermediate variables, especially the cost or

productivity.

2.1.1.4 Review of the Relationship between Productivity and Profit

Although some researchers, as previously described, may doubt that better

quality leads to higher productivity and hence increases profit, it is significant that no

one suspects that increasing productivity would reduce profit. It seems that everyone,

including managers and workers, believes firmly that productivity and profit have a

strongly positive relationship. The following review of the relationship between

productivity and profit also supports this belief

In 1911, Taylor, a man of great insight pointed out that the lack of

productivity undoubtedly resulted in a great loss to the society. From Taylor's work,

it can be implied that there is a positive relationship between productivity and profit.

Buehler and Shetty (1981) state that "At the company level, productivity is the key to

profitability" (p. 17). Feigenbaum (1983) regards productivity as one factor of

profitability. Kantzan (1985) thinks that it is obvious that productivity is directly

25

related to profitability. Sink (1985) suggests seven performance measures of an

organizational system- quality, profitability, and productivity are among them.^ He

believes these measures have a solid relationship amongst each other. Hayes (1985)

thinks that it is better to understand the relationship between productivity and profit

from a negative standpoint. That is, unproductive processes have a negative impact

on profit margins and have to be offset by additional sales. Deming (1986), who

regards productivity and quality as completely dependent, also believes that with

enhanced productivity, profit also increases. Cranberry (1987) defines productivity

as "measured by the price that must be charged for the product to produce an

acceptable level of profit" (p. 817). Belcher (1987) gives an example which

compares the profitability, price recovery, and productivity of two companies. He

concludes that the increase ofproductivity is sufficient to offset the decline of price

recovery, and hence results in profit growth. Edosomwan (1988) defines profitability

as changes in profits in terms of changes in total productivity and price recovery.

Smith (1990) presents examples ofproductivity ratios, some of which are measured

in terms of profit. Pritchard (1990) asserts that data used for measuring productivity

"must be reconcilable with profitability data" (p. 131). Karl5f (1993) also maintains

that productivity and profitability has a strong correlation.

^ The other four performance measures are effectiveness, efficiency, quality of work life, and innovation.

26

From the viewpoint of linking productivity and profit in a mathematical

model, Sumanth (1979) and Miller (1984) presented the most significant findings. In

his 1979 dissertation, Sumanth developed a model to show that profit is a fimction of

total productivity. He also introduces a concept of the break-even point in

determining total productivity. Sumanth found that the total productivity at the

break-even point was less than 1.0. In the dissertation, Sumanth fiirther proved that

the concept of "productivity-oriented profit" (POP), was the same as the concept of

conventional profit (COP). According to Sumanth, the difference between POP and

COP is that POP "considers revenues and costs in constant dollars of the based

period, whereas the COP is in current dollars" (p. 5.1). Sumanth (1980) later

presented a productivity benefit model to explain that the improvement of total

productivity in organizations can result in benefits to everyone, including consumers,

employees, stockholders, the society, and the nation. Based on Sumanth's findings in

his dissertation, Sumanth and Wardhana (1993) developed a mathematical

relationship model between quality of conformance, total productivity, and profit.

According to Kendrick (1984), the APC (American Productivity Center)

revised Von Loggerenberg's proposed basic system and presented a model of the

productivity-profitability relationship. This APC model is very similar to the

REALST model, developed by Von Loggerenberg at Data Resources Incorporated.

The APC model defines profitability as a fimction ofproductivity times price

recovery.

27

In 1984, Miller presented the PPP (Profitability = Productivity + Price

recovery) model, in which he defined profitability as equaling the sum ofproductivity

and price recovery. This model is theoretically similar to the APC's total factor

model. APC presented its model eariier than Miller's PPP model; however,

according to Miller and Rao (1989), there are a couple of differences between these

two models. First, the PPP model stresses the use of dollar figures, while APC's

model emphasizes the use of ratios. Second, the PPP model produces cumulative

values, whereas the APC model considers only a period-to-period data in the two

comparing periods. It does not take into account the inflation factor or sales prices in

the intervening periods. Miller (1987) believes that a company's true concern about

profitability is the return on investment (ROI), therefore, he also developed a model

to link productivity (total factor productivity) with profitability based on ROI.

In addition, other research is interested in developing the mathematical

relationship model of productivity-profitability. Adam, Hershauer, and Ruch (1981)

explain the relationship between productivity and profit by using an index of

profitability: a ratio of sales (output quantities x prices) to costs (input quantities x

unit costs). Papadimitriou (1992) also developed the Profit Decomposition Model

(PDM), in which the percent contribution of each determinant to profit growth is a

function of productivity, in addition to other variables. In the PDM model,

productivity contribution is further divided into two components: productivity

contribution due to scale and productivity contribution due to factor prices. Harmon

28

(1984), in her dissertation, agrees that productivity and profitability have a close

positive relationship. However, she added that the negative relationship, rising

profitability with declining productivity, may exist if there is a lot of backlog in

demand. She conducted a case study to investigate the relationship between

productivity and quality cost. Her study also demonstrates the positive relationship

between productivity and profit.

2.1.1.5 Review of the Relationship between Quality and Productivity

For many years, quality and productivity have been regarded as mutually

conflicting. Deming (1986) notes that it is typical for American management to

believe that the goals ofproductivity and quality conflict. As Belcher (1987) states,

"Management traditionally has viewed quality and productivity essentially as trade

offs" (p. 143). The explanation related to the negative correlation between quality

and productivity is noted in additional works. For example, "It is reasonable to think

that lowering quality standards will increase productivity because the amount of

'good' product made will increase slightly" (Kaydos, 1991, p. 22). Also, "On the one

hand, productivity is often synonymous with increased output. On the other hand,

thoughts of quality often conjure up visions of a quality control team insisting on

more careful production, resulting in decreased output" (Darst, 1990, p. 117). Or "It is

argued that a program to improve quality causes disruptions and delays that result in

^ She does not mention that another type of negative relationship, rising productivity results in declining profitability, may exist.

29

reduced output," (Omachonu & Ross, 1994, p. 179). But these explanations are

doubtftil. Hart and Hart (1989) pomt out that, "There is a misconception in the minds

of many people that quality and productivity are conflicting goals" (p. 3). Robson

(1990) states that many manufacturers believe that if they focus on productivity,

quality will be sacrificed. Sumanth and Arora (1992) also mention that the notion of

improved quality resuhing in a loss in productivity is a common fallacy in industries.

Most research indicates that the relationship between productivity and quality

is positive. Feigenbaum (1977) points out that, "a certain 'hidden' and non-productive

plant exists to rework and repair defects and returns, and if quality is improved, this

hidden plant would be available for increased productivity" (p. 21). Deming (1982)

makes an argument for the positive relationship between productivity and quality. He

believes that the reduced productivity resulted from quality defects, rework, and

scrap. Therefore, Deming concludes that the improvement of quality will transfer

waste of resources into the manufacture of good products. Christopher (1993) even

stresses that quality and productivity are inseparable. Hayes (1985) also thinks that,

"Quality and productivity are integrally bound and share common goals" (p. 59).

Garvin (1988) also agrees that a positive correlation between quaUty and productivity

does exist. He explains "Less rework means more time devoted to manufacturing

acceptable products, and less scrap means fewer wasted material" (p. 84). However;

he also points out that this explanation is too narrow and provides only limited

insight. Smith (1990) fiirther indicates that in order to reflect the conviction that

30

quality and productivity are related and occur simultaneously, the American

Productivity Center located in Houston was renamed the American Productivity and

Quality Center in 1988. Based on Boileau's (1984) experience as President of

General Dynamics, he concludes that quality and productivity are firmly related and

codependent. Barret (1994), Willbom and Cheng (1994), and Omachonu and Ross

(1994) all assert that productivity and quality are closely related.

Most of the assertions that quality and productivity are positively related are

based on the position that productivity is improved through the improvement of

quality. In other words, many researchers and managers believe that quality

improvement must precede productivity improvement. As mentioned in the previous

paragraph, Deming (1982) believes the reduction in productivity was caused by the

defects, rework, and scrap. In order to promote continuous improvement. Ford Motor

uses six guiding principles based on Deming's fourteen points for top management.

The first of these principles is "Quality comes first"'^ (Shetty & Buehler, 1985, p.

149). Shetty and Buehler (1985) believe that one of the characteristics of high-

performance companies is, "Quality improvement is a catalyst for productivity

improvement," (p.325). L. Jerry Hudspeth, Vice President of Productivity and

^ Sumanth (1994), who coined the term PQ team, or PQTs (productivity and quality teams), maintained that PQTs place more emphasis on productivity and quality than QC circles, although they both improve quality and productivity. However, he did not claim that quality was improved by the improvement ofproductivity.

'^ The other five principles are customer focus, continuous improvement, employee involvement, surpass competitors in overall performance, and partnership with suppliers/dealers. Here we see the emphasis placed on putting quality first. That is, quality before productivity.

31

Quality at Westinghouse Electric Corporation and the first director of the

Westinghouse Productivit>' and Quality Center, indicates that 'whenever you find you

have a problem with productivity, it usually translates into a dimension of quality"

(Ryan, 1983, p. 6). Butts (1984), in his paper "The relationship of quality to

productivity," describes poor quality as "a vampire-like creature which takes bite

after bite out ofproductivity" (p. 38). Pantera (1985) asserts that quality is the key to

productivity. Garry (1985) stresses that "the quality road to productivity is the

shortest and most effective route to higher productivity" (p. 90). Ferchat (1987)

regards productivity as an issue of quality. Townsend (1990), who believes quality

and productivity are different, affirms that "quality incorporates productivity" (p. 7).

He emphasizes that only through quality improvement can productivity be enhanced.

Tribus (1992) points out that the route to increase productivity is through increasing

quality. He further states that, "if you want productivity you have to focus on quality

first" (p. 98). Hayes (1985) writes "Quality influences productivity by its effect on

profit, and drives it two ways: (1) quality influences sales and consequent income

from such sales..., and (2) quality increases internal efficiency and capacity by the

degree that sundry corrective actions are prevented" (p. 59). Barrett (1994) states

that, "An increase in the quality,..., of a product or a service at no added cost

constitutes a productivity gain" (p. 128). Hart and Hart (1989) think that with

improved quality, increased productivity will follow. Gitlow (1990) believes that

emphasizing only productivity will sacrifice quality and may even lower output.

32

Darst (1990) stresses that following correct procedures to ensure quality will result in

heightened productivity. Sumanth and Arora (1992) review the literature and

conclude that "improvements in quality lead to improvements in productivity" (p.

151). Omachonu and Ross (1994) attribute the misconception that increased quality

results in decreased productivity to those who rank productivity higher than quality as

the top priority in production. Therefore, it can be deduced that, "productivity and

quality have a direct relationship. As quality increases, productivity increases ~ not

the other way around," (Kaydos, 1991, p. 22).

Not many studies can clearly describe the relationship between quality and

productivity in detail because it is difficult to reach a consistent definition for

various companies.'' Lawler and Ledford (1983) indicate that even though "There is

wide agreement about the conceptual meaning ofproductivity, the major difficulties

are in applying the concept to specific organizations" (p. 5). Garvin (1988) says that

the best way to understand the relationship between quality and productivity "requires

an examination of their common sources of improvement" (p. 84). He further

indicates that there are few systematic studies on the relationship between quality and

productivity. Belcher (1987) indicates that the problem lies in the definition.

Hoffherr, Moran, and Nadler (1994) think productivity lacks a clear-cut definition

that can be used as a basis for measurement and aggregation. Therefore, it is obvious

' ' Sumanth (1994) classified various definitions and interpretations ofproductivity into three basic types. Partial productivity, Total-Factor productivity, and Total productivity. However, he did not mention that the definition of quality could also be unified.

33

that the relationship between quality and productivity is, as Smith (1990) claims,

dependent on how the definitions of each concept are expressed.

Because quality and productivity are so directly related, some people think

that the two are nearly the same. Adam, Hershauer, and Ruch (1981) state that,

"Frequently, scholars and practitioners alike refer to 'productivity' and 'quality' as if

they were two separate performance measures. Yet a significant part of any

producfivity equation is quality" (p. 12). Shetty and Buehler (1984) point out that the

Japanese regard quality and productivity as two neariy synonymous terms. Kaydos

(1991) thinks that productivity and quality are neariy synonymous. Thor (1993)

illustrates process quality and productivity are essentially the same. In their articles,

Katzan (1985), Smith (1986), Price (1989), and Federal Express (1993) all firmly

claim that quality equals productivity.

Although the relationship between productivity and quality is thought to be

positively correlated, it varies depending on how each concept is defined (Smith,

1990). Shetty and Buehler (1985) point out that productivity and quality are not new

ideas, but most companies have not clearly defined these terms.'' Harrington (1987)

thinks that the ideal indicator for measuring quality and productivity simultaneously

is to measure "the sum of all inputs divided into the quantity of output that met

customer expectations" (p. 104). However, it is difficult to calculate this ideal

indicator. Because of the various functions and activities in different departments

' In order for both quality and productivity to be organizationally effective terms, they must be operationally defined For further information on operational definitions refer to Deming (1986)

34

and companies, unless specifically defined, a universal fimction of the relationship

between quality and productivity can not be developed. However, Thor (1991)

provides his principles of measurement for both productivity and quality:

• Meet the customer's need; • Emphasize feedback directly to the workers in the process that is being

measured; • The main performance measure should measure what is important; • Measures should be controllable and understandable by those being

measured, and • Base measures on available data. If not available, apply cost benefit

analysis before generating new data.

Mohanty and Yadav (1994) believe that Total Quality Management is the base

to provide integration of quality and productivity. They also suggest some ways to

link quality and productivity:

• Viewing customer as the future assets of an organization; • Identifying and providing flexible responses to the needs of the

stakeholders; • Adding value at each stage of each operation; • Fostering respect for the human system; • Shifting emphasis from maximizing individual capitalist gains to

improving quality of life for the society as a whole.

Sumanth and Arora (1992) also propose a conceptual framework to illustrate

the quality-productivity link. In addition to the descriptive method, if quality and

productivity are specifically defined, a mathematical model linking quality and

productivity can be developed. By measuring quality as quality of conformance and

by defining productivity as total productivity, Sumanth and Wardhana (1993) present

a mathematical quality-productivity relationship model. From the results of the case

35

study in her dissertation, Harmon (1984) concludes that a firm's productivity has a

definite relationship to the product quality.

However, Kendrick and Creamer (1965) has indicated that after the Worid

War II, many companies obtained higher profitability v^th less productivity because

of the backlog in demand. This situation, again, shows that the market influence can

reverse the positively correlation between quality and productivity. Therefore, when

discussing or developing the relationship models among quality, productivity, and

profit, it is important to consider the market influence first.

2.1.2 Definitions

Before developing the relationship between quality and productivity, it is

helpful to examine the definitions of these two terms. Although they are not new

concepts, people have created different definitions for each term. These definitions

are arranged in two tables (Table 2.1 and Table 2.2). In addition, since this research

is to link quality and productivity based on profit, summarized definitions of profit

and profitability are also listed in a table (Table 2.3). All definitions in both tables

are listed in chronological order. By examining these definitions, some findings

related to each term are also addressed.

36

2.1.2.1. Definitions of Productivity

Table 2.1 presents some significant definitions ofproductivity in the open

literature. From these definitions, several points can be concluded:

1. The core definition ofproductivity is the ratio of output to input.

2. Productivity ratios vary in measurement units. They can be measured in

%, dollars per hour, pieces per day, etc. If productivity ratio is measured

in revenue per cost, then it directly relates to profitability.

3. Productivity can only be measured for tangible inputs and outputs.

4. For different purposes of measuring productivity, there are a number of

different measurement approaches.

5. Productivity is closely related to effectiveness and efficiency.

6. The output ofproductivity assumes valuable product or services. That is,

the output does not include the valueless. Based on this assumption, it is

possible to relate productivity with quality.

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2.1.2.2. Definitions of Quality

Table 2.2 provides the important definitions of quality in the open literature.

From these definitions, five points are worth noting:

1. All the definitions in this table show that quality is an abstract term, and

is not measurable.

2. Some (e.g., Pirsig, 1974) believe quality cannot be defined, while

others believe that it should be defined by situation (e.g., Deming,

1986).

3. Most definitions demonstrate that quality is customer-oriented.

4. Quality can be defined from two aspects; external and internal

environment. Definitions related to the customer are defined from the

external aspect (e.g., Juran's "customer satisfaction"). Definitions

not related to the customer are defined from the internal aspect (e.g.,

Gilmore's "conforms to a design or specification").

5. No definition of quality in the open literature was found to relate directly

to profit.

43

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2.1.2.3. Definitions of Profitability and Profit

Table 2.3 presents the definitions of profitability and profit. From this table,

five points can be summarized;

1. Profitability is directly related with productivity.

2. Quality is not directly related with a measurable profitability.

3. Profitability can be measured in terms of various units.

4. Profit and profitability are similar terms. Therefore, unless specified in

models, profitability and profit cab be viewed as interchangeable terms,

especially when comparing the relationships with quality or productivity.

5. At firm's level, profit is the result of all combined efforts in a company.

Therefore, unlike productivity, no 'Total-Factor Profitability' or 'Partial

Profitability' is found in the open literature.

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52

2.2 Current Profit-Based Quality, Productivity Models

In this section, the current relationship models regarding quality, productivity,

and profit are presented. Since no quality-profit model is found in the literature

review, and cost is closely related to profit, the quality-cost relationship models are

addressed instead of quality-profit model. These quality-cost relationship model are

presented in subsection 2.2.1. In subsection 2.2.2, the productivity-profit relationship

models are presented. All of the productivity-profit models found in the open

literature demonstrate the positive relationship between these two variables. The

third subsection illustrates the current quality-productivity relationship models, not

restricted to profit-base.

2.2.1 Quality-Cost Model

Intuition dictates that higher quality should produce more profit. However,

unfortunately, no such direct relationship expressed in a model or fimction can be

found in the literature review of this research. Research on the relationship models

between quality and profit are mainly fi-om the cost viewpoint. In this subsection,

four models regarding the quality-cost relationship are presented: Juran's Optimum

Quality Cost Model, Dawes' Quality-Cost Model, Harrington's Poor-Quality-Cost

Model, and Taguchi's Quality Loss Function Model.

53

2.2.1.1 Optimum Quality Cost Model

Juran (1974) presents a model (shown in Figure 2.1) for optimum quality

costs. In this model, total quality costs is the sum of failure costs, appraisal costs, and

prevention costs. The optimum quality level is determined at the lowest total quality

costs. A product manufactured at the optimum quality level can not only fit the

customer's use, but also cost the least. This implies that the product manufactured at

the optimum quality level will result in more profit.

o -o O <-«

C+H

O

c ff

o o GO VH

<D Cu

• * - ^

Vi O u

To infinite

Total quality costs

Failure costs

Costs of appraisal plus prevention

To infinite

Quality of conformance, % 100

Figure 2.1 Model for Optimum Quality Costs. (Source: Juran, 1974; p. 5.12).

This model has been modified by Juran (1988). In Juran's former model, it

seems that the optimum quality level can never become 100% of conformance, which

is especially emphasized by modem management. Therefore, Juran (1988) modified

his own model as shown in Figure 2.2. In this new model, three points are worth

54

noting: (1) The prevention costs are stressed more, (2) The appraisal costs are

reduced because more elaborate testing equipment and advanced inspection

techniques have been employed, (3) The introduction of new technology has reduced

the potential defects inherent in the product, and hence lower the failure costs. This

new model emphasizes that the optimum quality level, still at the lowest total quality

costs, is 100% of conformance. Since higher conformance is reached at the same

time as the lowest costs, more profit is produced.

o T3 O Q .

» • -O

T3 O O O) v _ (D Q .

V) O

O

Total quality costs

Costs of appraisal plus prevent!

Failure costs

Quality of conformance, % 100

Figure 2.2 New model for Optimum Quality Costs. (Source: Juran, 1988; p. 4.19).

2.2.1.2 Dawes' Quality-Cost Model

Dawes (1987) presents a Quality-Cost model as shown in Figure 2.3. This

model revises Juran's (1974) model based on the conviction that "Perfection is

55

possible" (p. 378). According to his experience, Dawes, the Quality Manager of

Haydon Incorporated, indicates that a successful company improves profit by using

an effective quality cost system. The improvement of quality cost is never ending.

Therefore, "perfection," the goal of continuous improvement, is likely to be

achieved.

TOTAL QUALITY COSTS (TOO

FAILURE COSTS (F) OLD

CONCEPT

TQC = P & A + F

NEW CONCEPTl

PREVENTION AND APPRAISAL (P & A

0% DEFECTIVE

100% CONFORMANCI

Figure 2.3 Dawes' Quality-Cost Model. (Source: Dawes, 1987; p. 381).

Dawes' model is similar to Juran's new model. However, Dawes believes

that "the processes of improvement and new loss prevention are, in themselves,

subject to increasing cost effectiveness" (p. 380). Therefore, Dawes emphasizes that

56

total conformance can be achieved without a disproportionately high resource cost.'"*

Juran's new model does not point out this concept.

2.2.1.3 Poor-Quality Cost (PQC) Model

Harrington (1987a) defines Poor-Quality Cost (PQC) as "all the cost incurred

to help the employee do the job right every time and the cost of determining if the

output is acceptable, plus any cost incurred by the company and the customer because

the output did not meet specifications and/or customer expectations" (p. 5). He

indicates that PQC is different from the traditional quality cost because PQC talks

about the cost of not having quality. However, he also indicates that PQC primarily

consists of the four types of quality cost: prevention cost, appraisal cost, internal

error cost, and external error costs.

Harrington classifies PQC into three types of costs: Controllable PQC,

Resultant PQC, and Equipment PQC. Controllable PQC includes prevention cost and

appraisal cost, while Resultant PQC consists of internal and external error costs.

Equipment PQC is the total cost of investment in equipment and the space the

equipment occupies.

Cost can be classified into direct and indirect costs. Since the indirect PQC

cost data is difficult to obtain and it occupies only a smaller part of total PQC,

Harrington focuses mainly on direct PQC.

' Dawes (1987) describes resource costs as the sum of prevention costs and appraisal costs

57

Hamngton explains how a maximized ROI can be reached fi-om the PQC

curve (see Figure 2.4). He believes that "An effective quality system should operate

at the point on the curve labeled 'best interim operating point'" (p. 31).

High DIRECT PQC CURVES

o Q

Lx)w Controllable Poor-Quality Costs

High

Controllable PQC

Resultant PQC

Combined controllable and resultant PQC

Figure 2.4 Effect of varying controllable PQC. (Source: Harrington, 1987a; p. 30).

58

2.2.1.4 Taguchi's Quality Loss Function Model

Taguchi's Quality Loss Function (QFL) model is one of his two famous

quality tools. ' He believes that if a product wears out or breaks and needs to be

repaired or replaced, then this results in a loss. This loss is eventually imposed on

society after the product is shipped. Therefore, Taguchi claims that a high quality

product causes little loss, while a low quality product results in great loss. He

believes that lower cost is the driving force behind quality.

Taguchi's QLF is in the quadratic form:

L(Y) = K(Y-T),' [2-1]

where Lisa loss function of Y

Y is the value of quality characteristic

T is the product's target value

K is a constant.

This quadratic function can be explained by the following Figure 2.5.

i

L(Y)

LSL: Lower Specification Limit USL: Upper Specification Limit v^^

LSL T USL Y

Figure 2.5 Taguchi's Quality Loss Function (Source: Taguchi, 1985)

"* The other is the Signal-to-Noise (SN) ratio used in the design of experiment.

59

In Taguchi's QLF concept, the loss is zero if the target value of the quality

characteristic is exactly at the central limit. In other words, at this point, the profit is

maximized. Therefore, the management should reduce the product's variability as

much as possible in order to maximize profit.

2.2.2 Productivity-Profit Model

As previously stated, no one questions the positive correlation between

productivity and profit, especially when output is measured in terms of dollars.

However, because of the variety ofproductivity measures, no universal model

regarding productivity-profit can be achieved. In this subsection, six productivity-

profit relationship models are addressed: Adam-Hershauer-Ruch's model,

Papadimitriou's Profit Decomposition Model, Sumanth's model, the APC model.

Miller's model, and Miller's ROI-based model..

2.2.2.1 Adam-Hershauer-Ruch's Productivity-Profitability Relationship Model

Adam, Hershauer, and Ruch (1981) explained the relationship between

productivity and profit by defining profitability as a ratio of sales to costs.

First, they define sales as the total output quantities times prices, and costs as

the total of each input quantities times unit costs.

Therefore, profitability is defined as

60

Sales _ Output quantities x prices

Costs Input quantities x unit costs '

Equation [2-1] can be rewritten as

Sales Output quantities Prices 7; = ~i — : X [2-31 Costs Input quantities Unit Costs

Adam, Hershauer, and Ruch view the ratio of'Output quantities' to 'Input

quantities' as 'Productivity'. They also regard the ratio of'Prices' to 'Unit costs' as

'Price Recovery'. Therefore, equation [2-3] becomes equation [2-4], which is

identical to APC Model ( described later).

Profitability = Productivity x Price Recovery [2-4]

2.2.2.2 Papadimitriou's Profit Decomposition Model (PDM)

Papadimitriou (1992) presented the Profit Decomposition Model (PDM). The

derivation of this model is illustrated as follows:

1st step: Papadimitriou defines profit as the difference between total sales

and total costs. This definition can be written in a formula:

^ = PQ-lLPiqi [2-5]

where ;r= Profit

P = Sales price

Q = Volume

61

Pj = The ith Input price

q, = The ith Input quantity

2nd step: By first totally differentiating, equation [2-5] becomes equation [2-

6].

dTT = PdQ + QdP - Y.Pidq. - Y.<iidp, [2-6]

3rd step: Multiplying equation [2-6] by successive terms of one in the form of

d;r=PdQxQ/Q + QdPxP/ P-Yj^,dq. xq, /q, -Yjii^P ""PlP [^'^l

Equation [2-5] can also be rewritten as

P = i [2-8] Q

Replacing equation [2-8] into equation [2-7] yields

d;r = 7dQ/Q+PQdP/ P+Y^Pi^MQIQ-'^t / < )-Y.Piqi^P 'P [2-9]

where ndQ IQ = Volume contribution

PQdP I P = Sales price contribution

YjPiî ^^0/ Q-^î lî)^ Multi-factor productivity contribution /•

Y^PiRi^Pi I Pi ^ ^"P^^ P"^^ contribution.

62

4th step: Papadimitriou believes that in the real environment, discrete data is

frequently used and the changes in data values are large. Therefore, he claims that

the equation [2-9] must be corrected by including interaction terms.

+ APAO-I.Ap.Aq. [2-10]

Equation [2-10] is the basic PDM.

5th step: Dividing equation [2-10] by last period's profit level yields equation

[2-11].

A;r ;rAQ/Q^PQAP/P . ^P'^^^^Q^0-^^'^^'^

;r(-l) 7r{-\) ;r(-l) ;r(-l)

-^ + . [2-11]

7t{-\) 7r{-\) 7r{-\)

Equation [2-11] indicates the percent contribution of each determinant to the

growth in profits.

6th step: The third term of equation [2-10] can be further decomposed into

two components: productivity contribution due to scale and productivity contribution

due to factor prices. That is,

Y,P^qA^QiQ-^q:iqi) = [ Y.qA^QiQ)-^q.iqi ] +

[ ZA'?,(Ae/e'-A?,/?,)-(Z'7,A(?/C?-A^,/</,) 1- [2-12]

63

The terms in the first bracket of the right-hand side of equation [5-11] is the

productivity contribution due to scale, while the first term in the second bracket is the

productivity contribution due to factor prices.

Papadimitriou points out that the decomposition demonstrates an increase of

factor price can offset the decline ofproductivity grov^h. This will resuh in an

increase in profit growth due to productivity. Therefore, Papadimitriou stresses that

"productivity does not have to increase at an increasing rate for the productivity

contribution to profit growth to increase" (p. 63).

2.2.2.3 Sumanth's Productivity-Profit Relationship Model

Sumanth (1979) developed a mathematical relationship model of Total

Productivity and profit. His model is as follows:

Profit P = TP(I) - ( IH + IM + Ic.F + IE + Ix ), [2-13]

where,

TP : Total Productivity

0 O TP = —= - [2-14]

1 IH + IM + IC.F + W + IE + x

where,

O : total tangible output

I: total tangible input

IH : human input

64

IM : material and purchased parts input

Ic F: fixed capital input

Ic,w : working capital input

IH : energy input

Ix : other expense input.

If total output is held constant, then equation [2-14] becomes

P = 0 - ( I H + IM + IC,F + IE + IX), [2-15]

P = 0 - r [2-16]

where, I ' : input costs other than working capital.

Because O is constant, there is a linear negative relationship between I'

and P (see Figure 2.6).

According to equation [2-15] or [2-16], Sumanth's model illustrates the

relationship between Total Productivity and profit: Profit increases as output

increases and/or input decreases.

65

Profits ($)

Profit Curve at q (increased output level)

- Profit Curve at q, (base period output level)

Profit Curve at q, (decreased output level)

Increasing Output

Input Costs Other Than Working Capital

Figure 2.6 The Relationship between Profits and Input Costs. (Source: Sumanth and Wardhana; pp. 463-474).

66

2.2.2.4 APC's Productivity-Profit Relationship Model

American Productivity Center (APC) presented a productivity-profit model in

the early 1980's. This model revised a basic system proposed by Basil Von

Loggerenberg and developed it into a model. The following describes this model:

First, define

Output Value = Quantity Sold x Unit Price, [2-17]

Input Value = Quantity Used x Unit Cost, [2-18]

Output Value o im and Profitability = ^ \^^ ,—, [2-19]

Input Value

Quantity Sold o ^m Productivity = . „ ., [2-^^l

Quantity Used

Unit Price n l^^ Price Recovery = _. .^^ ^ • L - 11

Unit Cost

Then the productivity-profit relationship become:

Profitability = Productivity x Price Recovery. [2-22]

It is obvious that this model shows the positive correlation between

productivity and profit.

2.2.2.5 Miller'^ Productivity-Profit Relationship Model

Miller (1984) also developed a productivity-profit relationship model similar

to APC's model. However, as described in Section 2.1.1.4, Miller's model has two

67

significant points which differ fi-om APC's model. First, Miller's model uses dollar

figures in both profitability, productivity, and price recovery, while APC's model

uses ratios. Second, Miller's model produces cumulative values, whereas the APC's

model considers only period-to-period data when comparing two periods. That is,

APC's model does not take into account the inflation factor or sales prices in the

intervening periods.

Because of these two different points. Miller presented his model in this form:

Profitability = Productivity + Price recovery,^ [2-23]

where

Productivity contribution in period t = (SalesDt) (MarginDt

- Margins), [2-24]

where

SalesDt: the deflated net sales in period t

MarginDt: the deflated gross profit margin in period t

Margins : the profit margin ofthe base period.

Price recovery contribution in period t = (SalesPRt)(MarginPRt

- Margins), [2-25]

where

SalesPRt: the price-generated revenue in period t.

' Note the right side of equation is the sum ofproductivity and price recovery In the APC model, equation [2-22], the right side of equation is a product ofproductivity and price recovery

68

MarginPRt: the price margin that equals the difference

between price-generated revenue and inflation-

generated cost divided by price-generated revenue.

Profit change = actual profit - anticipated profit, [2-26]

or

Profit change in period t = (salest)(margint - margins). [2-27]

Miller's model also illustrates the positive relationship between productivity

and profit.

2.2.2.6 Miller's Productivity-ROI Relationship Model

Miller (1987) believes that "a firm's true criterion of profitability is return on

investment (ROI)" (p. 1051). Thus, he presents a model based on ROI to modify the

profit-linked models.

First, Miller formulates the profitability change P, as

P, = (Sf - O - [ { S ^ -C4)l Ii)]{lf) [2-28]

where S = Net sales

C = Cost

I = Capital Investment

A = Actual dollar amount

B = Base period index

t = time period index.

69

Equation [2-28] can be rewritten into equation [2-29] by multiplying the unit

quantity (.Sg / S'^).

Â rÂ p,=i^:-c:)-Mis',{p;ni) [2-29]

.4 icÂ where M'^ = Profit margin = 1- QIS^

Second, equation [2-29] can be refined by partitioning A into price (or

inflation) component (denoted by superscript P) and quantity component (superscript

D). Therefore,

/ = (5,^-cf)+(5;-c;)-M^ 0.4 O.J

ID ' D

[2-30]

£) _ C--1 jD _ jA Third, because at base period 5, = S] , /, = /,

^ . 1 o D

= s? DrrD =srT, [2-31]

where, T,^ = ^ ^ , is the indexed change in deflated or real

S, II,

capital turnover in period t.

Replacing T,^ into equation [2-30], yields equation [2-32].

P. = [ (Si'-Cn-M-iSfT,' ] + [ ( 5 ; - C ; ) - M X / r ] [2-32]

The two terms in the first bracket stands for the productivity component,

while the two terms in the second bracket represents the price recovery component.

70

Fourth, the productivity component can be rewritten by subtracting M^SJ^

fi-om the firs term (Sl" - C,^), and adding M^Sl" to the second term M^SJ'T,''. This

yields equation [2-33].

K=[ {S:'-C^)-MXT^' ] + [ M^Sl^il-T,^) ] [2-33]

where F, is the productivity contribution in period t.

According to Miller (1987), the first term in equation [2-33] is "the same

productivity component as is used in the marginal approach" (p. 1502). He further

indicates that "the growth in ROI can be analyzed in terms of a margin goal for real

or deflated productivity performance, as well as a margin goal for capital investment"

(p. 1502-1503).

2.2.3 Quality-Productivity Relationship Models

In this section, several Quality-Productivity models are addressed. As Garvin

(1988) points out, research on the relationship between quality and productivity are

few, all the models regarding Quality-Productivity relationship are presented. The

most significant model to this research is the Sumanth and Wardhana's Quality-

Profit-Productivity model. This model is the only model that discuss the Quality-

Productivity relationship based on profit. Before Sumanth's model, four models are

first presented. These four models are Adam-Hershauer-Ruch model, Deming's

model, Edosomwan's model, and Thor's model.

71

2.2.3.1 Adam-Hershauer-Ruch Model

Adam, Hershauer, and Ruch (1981) developed the quality-productivity ratios

(QPR) to measure the effectiveness and efficiency of quality activities. Their model

includes three ratios, QPRl, QPR2, and QPR3.

^r^^, Nunter of items not idected QPRl^ [Tctel iiinixr of itore X Axx»sii^ cc3St pff ilen^+[Niiite of OTo-it^

[2-34]

^^^ Number of items not rejected OPR2 = —- r'?-' 51

Total number of items x Processing cost per item

Number of items not rejected QPR3 =- : ; ; r - —. : [2-36]

Total number of items x Reject processing cost per item

Generally, QPRl is very close to the concept ofproductivity - the ratio of

output to the input resources. The output is the number of good items; the input

resources are the total resources required to initially produce both good and bad items

plus the resources consumed to transform the items from bad to good. QPR2 and

QPR3 are the components of QPRl, the basic measure.

i e — ^ = — — + • [2-37] ' QPRl QPR2 QPR3

Sumanth (1994) regarded this model as the cost unit approach to measuring

productivity.

72

2.2.3.2 Deming's Model

In 1950, Deming (1986) presented a chain reaction concept related to quality

and productivity. He taught this concept in every meeting with top management in

Japan. This chain reaction is described in Figure 2.7.

Improve

quality } Costs decrease because

of less rework, fewer mistakes, fewer delays, snags; better use of machine-time and materials

} Productivity^

improves

Capture the market with

better quality and lower pnce }

Stay in business }

Provide jobs

and more jobs } Figure 2.7 Chain Reaction Related to Quality and Productivity. (Source: Deming,

1986; p. 3)

This model indicates that the improvement of quality usually breeds the

improvement ofproductivity. This model is conceptual in nature and provides as

mathematical support.

2.2.3.3 Edosomwan's Model

Edosomwan (1988) developed a productivity and quality management model

(PQMN). First, he constructed a framework (see Figure 2.8) for understanding the

73

Finished units

produced

I

Partial units

produced

I

Other income

associated with units produced

Customer dissatisfactio

I

Prototype and other

output associated with units pro4uced produ

Productivity =

n 1 H Output

Customer satisfaction

Input

Poor supervision

Rework

Engineering changgs Poor training Inspection cost spect

St Process delays Scrap

Warranties charges

£ r cr o c •-t

N /

N /

v/ s / N /

v/ ^/

I c\>

s/

y v/ v / v / v / x/ v /

I n p

v/ N /

3 CD •-I

v/

x /

N /

H a o 3 o

e?

s/ > /

x /

I H •-I

5' 5'

OQ

N /

v/

v /

x /

cr l-l

X o 1/3

C/3

v/

v /

Good supervision

No rework

No engineering changes cnange Uopd training Decreased insection Optimised t?rocess

No scrap

E oor quality # Quality measure of value (% defective) #(jOod quality

Figure 2.8 A Framework for Understanding the Connection and Relationship between Productivity and Quality. (Source: Edosomwan, 1988; p. 93).

74

connection and relationship between productivity and quality. In order to achieve

excellence in productivity and quality, Edosomwan (1988) pointed out that the lever

of productivity and quality must be balanced and kept at a high level. In addition, he

developed a productivity and quality assessment matrix (PAQAM) which companies

use to evaluate the balancing status of these two measures. He also presented a five-

step approach for the using of PAQAM in the work environment. The five steps are

as follows:

Step 1: Train everyone on productivity and quality management concepts and techniques.

Step 2: Develop and implement measurement methods for productivity and quality at the individual, task and organizational levels.

Step 3: Classify the productivity and quality measures obtained in Step 2 in four major categories: poor, fair, good, and excellent. Plot the values obtained in the PAQAM assessment matrix.

Step 4: Perform a root cause analysis to determine why a particular performance appears on each region. Implement improvement actions to correct and move a poorly performing individual or task to the region ofproductivity and quality excellence.

Step 5: Follow up periodically on open issues. Train everyone in the organization to use PAQAM to assess his ovm productivity and quality position. (Edosomwan, 1988; p. 100).

To express the quantitative relationship between productivity and quality,

Edosomwan (1988) also developed a correlation coefficient formula of PAQAM:

TO TP, = - ^ ^ [2-38]

ID; n ( n ^ - l )

RCC, = l - 6 x - f V - T : [2-391

75

[2-40] sec. = ^ L '-' '-' Jr^lP- -(IP.Y Jn^Q^ -(±Q,y V 1 = 1 i = l V i = l i = l

Where,

TOit= Total output of task, i, in period, t.

Tl{f= Total input utilized to produce output of task, i, in period, t.

TP{f= Total productivity of task, i, in period, t.

QIit= Quality index of task, i, in period, t.

(Pi Qi)= Paired productivity and quality data for each individual

performing task, i, in period, t. (i=l, 2,..., n)

Di2 = The difference between the ranks assigned to P{ and Q{

SCCit= Sample correlation coefficient for paired data (P Qj)

assuming bivariate normal population.

RCCit= The rank correlation coefficient that can be used to compare

Pj and Qi ML = Maximum likelihood function that can be used to obtain the

mean, variance and CCit (correlation coefficient) of (Pi Qi) n

paired data by differentiation method, i.e. ML = J j f(Pi ,Q,). i = i

Finally, Edosomwan (1988) analyzed the components ofproductivity

management and quality management in the PQMM as shown in Figure 2.9. This

model was developed so that management could control productivity and quality at

the source.

76

A: Productivity management

Productivity mix, defect rate, system rate and other productivity and quality parameters referenced to the same base period

Productivity and quality measuremen Evaluation and control of process parameters

Input •Labour •Materials •Computers •Roborics •Capital •Energy •Other forms of technology 'Administrative and other

B: Quality management

Supplier requirements for productivity and quality, acceptable input rate and qualify leyek

Productivity and quality simulator and control limits

On-going action on the input process

Productivity anc quality planning of process parameters

Transformation process

Process technology

Man-machine interface

Standard-alone tool

Interactive mechanism'

Others

Process parameters •Flexibility •Demand/supply rate •Speed of mechanisms •Complexity of tools •Yield/reliability •Others

Management information system Data base for production, services and systems paratemers

I On-going action on the transformation process

Productivity and quality improvemen Monitoring of process parameters

Output •Finished units produced •Partial units produced •Other useful services and gains associated with inputs

Customer requirements for productivity and quality, acceptable output level and out-going quality t Total system control rate of production and service must be equal to rate of consumption

On-going action on the output process

Control system for balance all process parameters that affect productivity and quality

Figure 2.9 Components ofthe PQMM. A: productivity components; B: quality components. (Source: Edosomwan, 1988; p. 99)

77

2.2.3.4 Thor's Model

Thor (1993) believed that process quality and productivity were

fundamentally the same. He depicted the relationship between quality and

productivity as shown in Figure 2.10.

Product and Service Quality

i i

Process Quality

Customer Expectations

< •

^ . . . . . . . . . . . . . . ^ ^ . . . . . . . . . . . . . . ^

Employee Effort

Technology

Lower Cost

ii

Productivity

Figure 2.10 Process Quality and Productivity Are Essentially the Same. (Source: Thor, 1993; p. 8-2.2).

He then presented a complete productivity and quality measurement system as

shown in Figure 2.11.

78

Productivity Measures

Corporation/Division Total Factor Productivity

7 Total Sytem Partial

Total Sytem Partial

X Planning

Total Sytem Partial

or or or Screening

Labor Total Productivity

Labor Partial Productivity

Control

Quality Measures

Corporation/Division Total Cost of Quality

lure, (aste, or

^reventio i

X [otal >vtem lilure,

./aste, or 'reventioi i

or or or

Labor Cost of Quality

Local Failure and Waste Rates and Local Prevention Cost

0/L, 0/M, 0/V, 0/K, 0/E

0/L, 0/M, 0/L, 0/M, O/V 0/V

Factory Floor

Sales/ Distribulioi i

Suppor Staff

W^W9i F/0,W/0, F/0,W/0, P/0 PCM, P/0 PC\i P/0 PCM, PQM SQM SQM Factory Floor

Sales/ Distributioh

Suppor Staff

0/L=Output/Labor Input 0/M=Output/Materials 0/V=Output/Variable Cost 0/K=Output/Capital 0/E=Output/Energy

F/0=Failure/Output W/0=Waste/Output P/0=Prevention/Output PCM=Process Control Measures PQM=Product Quality Measures SQM=Service Quality Measures

Figure 2.11 A Complete Productivity and Quality Measurement System. (Source: Thor, 1993; p. 8-2.4).

79

2.2.3.5 Sumanth and Wardhana s Quality-Profit-Productivity (OPP) Relationship Model

Sumanth and Wardhana (1993) developed a mathematical relationship model

between Quality of Conformance, Profit, and Total Productivity (QPP). This model

is based on the Dawes' model and Sumanth's total productivity model, break-even

point of total productivity, and productivity-oriented profit. This model measures the

quality-profit relation through the interaction with total productivity.

By using this model, the effects of a changed output on the total productivity

and profit can be measured at a fixed level of quality of conformance.

The QPP model is developed as follows:

1. Develop a mathematical relationship between total productivity and profit.

This model, developed by Sumanth (1979), has been stated in subsection

2.2.2.1.

2. Divide each inputs of TP into five parts:

a. The portion ofthe input not directly related to the quality system (nq).

b. The portion ofthe input not directly related to appraisal cost (a).

c. The portion ofthe input not directly related to prevention cost (p).

d. The portion ofthe input not directly related to internal failure cost (if).

e. The portion ofthe input not directly related to external failure cost (ef).

Then,

80

J = (lH:nq + Iw.nq + Ic.F.nq + Ic,W:nq + Il-nq + Ix;nq ) +

(lH:a + lM:a + Ic,F.a + Ic,W:a + k:. + Ix:a ) +

( I H . P + IM;P + Ic .Fp + Ic,W;p + Ic.p + Ix;p ) +

( W + lM.a\ir+ Ic,F;,f+ Ic,W:,f + lE:if + Ix:if ) +

(iH.ef + iM.ef + IcJ^;ef + Ic.W;ef + lE.ef + Ix;er ) • [ 2 - 4 1 ]

That is,

l = I n q + I a + I p + I . r + I e f [ 2 - 4 2 ]

or

I = Inq + Iq [2-43]

where, Inq: total input not directly related to quality system

la : total input directly related to appraisal cost

Ip : total input directly related to prevention cost

I,f : total input directly related to internal failure cost

lef : total input directly related to external failure cost

Iq: total input directly related to quality system.

3. According to Dawes' model (revised Juran model), derive a relationship

between quality of conformance and input costs other than working capital. (See

Figure 2.12.)

4. Combine Figures 2-6, 2-12, then Figure 2-13 is developed.

81

Quality of Conformance

•

(100%

Total Non QuaUty + Quality Effort Curve

Input Costs Other Than Working

Capital ($)

At Quality of Conformance =Q2 %

AB = Costs of Non Quality Effort

BC = Costs of Prevention + Appraisal

BD = Costs of Internal + External Failure

BE = Total Costs of Quality Effort AE = r = Total Costs of Non Quality + Quality Effort

Other Than Working Capital

Note When Quality of Conformance improves to Q, total costs of non quality + quality effort dcrease to F,

Figure 2 12 Costs of Non-Quality and Quality Efforts as a F^^^ion of Quality of Conformance. (Source: Sumanth and Wardhana; pp. 463-474)

82

Quality of Conformance A

(100%)

Q,

(0%)

Profit ($)

Total Non Quality + ty Effort Curve

Profit Curve

Total Productivity

( $ / $ )

P3 (profit) TP

P, (=0) TP.

high)

(=TPBE)

P, (loss) TP low)

Figure 2 13 The Relationships between Quality of Conformance, Profit, and Total Productivity. (Source: Sumanth and Wardhana; pp. 463-474).

83

2.3 Deficiencies and Limitations of Current Models

In this section, the deficiencies and limitations ofthe current models, as

introduced above, will be to be discussed in the following order: Quality-Cost

models, Productivity-Profit models, and Quality-Product models.

2.3.1 Deficiencies and limitations of Current Quality-Cost Models

The current Quality-Cost models described in section 2.2.1 have the following

deficiencies and limitations:

1. Both of these models explain the relationship between quality and profit

from the cost viewpoint, not from the profit viewpoint. Although cost and profit are

very closely related, they are different. On one hand, the reduction of cost does not

necessarily result in increased profit. On the other hand, the increase of profit is not

necessarily based on the reduction of cost. There exist intermediate variables between

profit and cost. Price and market share are the two most influential intermediate

variables. Other intermediate variables (e.g., interest rate and tax rate) also have

effects on cost and profit, but are not as sensitive as price and market share.

The relationship between cost and profit can be illustrated by Figure 2.14. If

the price and market share are not increased, then increased cost will result in profit

decrease. Similarly, if the price and market are not decreased, then reduced cost

causes profit increases. Therefore, cost and profit are not directly related.

84

Cost Up

Cost Doyvn

\

Not relatively

Price

Price

increasing

Market share

Market share

Not relatively decreasing •

/

Profit Down

Profit Up

Figure 2.14 Cost-Profit Relationship

Since cost and profit are related through intermediate variables, it is not

appropriate to explain the Quality-Profit relationship by the Quality-Cost relationship

models unless the intermediate variables can be controlled.

2. All ofthe mentioned Quality-Cost relationship models relate quality to the

"quality cost," not to the "total cost." The concept of quality costs, initially called the

cost of quality, were first proposed by Juran (1951) in the "Quality Control

Handbook." Juran defined quality costs as the expenditures incurred because of poor

quality. It is obvious that quality costs and total cost are different concepts.

85

Profit IS produced by subtracting the total costs, not quality costs.

Furthermore, the current quality-cost relationship models determine the optimum

quality level fi-om the total quality costs viewpoint, not from the perspective of total

costs. Therefore, it is inappropriate to measure profit fi-om the quality-cost models

described previously.

3. The revised quality-cost relationship models, either by Juran or Dawes, all

indicate that the optimum quality levels are obtained at the lowest total quality costs.

This assertion is also doubtful.

First of all, their assertion is simply an ideal conceptualization. There is no

mathematical proof or practical evidence to support the notions indicated in the

models. In addition, since Juran and Dawes believe that the optimum quality level is

100% conformance, no defect is allowed. One ofthe reasons that the statistical

method is v^dely applied is that it can save time and costs in guaranteeing a product

reaches a certain quality level, but not 100 % conformance. No one can ensure 100%

conformance quality level with no risk. Under 100% confidence level, the confidence

interval of quality level must be between negative and positive infinity. This interval

is meaningless to management. Therefore, the quality-cost relationship model is just

an ideal model used to arouse the management examining the product quality issue.

4. Taguchi's loss function stresses that the loss incurred by poor quality will

eventually be imposed on society. This is an excellent concept in emphasizing the

importance of good quality; however, it cannot help a company to evaluate the degree

86

of loss incurred by poor product quality. Since the loss will be shared by all of

society, it is not a loss to a single company only. Therefore, the loss function is not a

measurable tool for companies to measure the loss caused by the poor quality.

2.3.2 Deficiencies and limitations of Current Productivity-Profit Models

The deficiencies and limitations ofthe Productivity-Profit Models introduced

in section 2.2.2 are summarized in the following.

1. The Adam-Hershauer-Ruch's model and the APC's model both measure

productivity in terms of quantity/quantity. This unit of measure is not consistent for

all the factors of input or output. For example, labor is one ofthe input factors and is

usually measured in terms of time consumed. Materials are also an input factor but

are meeisured in piece or money. Unless these two factors are being transferred in

terms of costs, they cannot be added together. Therefore, their models cannot

effectively be used in practical application.

Although the Adam-Hershauer-Ruch's model and the APC's model are

identical, they are interpreted differently. The Adam-Hershauer-Ruch's model

interprets productivity by the ratio of output quantity to input quantity, while the

APC's model explains productivity as a ratio of quantity sold to quantity used. The

former model implies that all the output produced can be sold wdthout difficulty in

the market. It seems not to take into account the market's response. On the other

87

hand, the APC's model considers the output from a sales standpoint, it also has

deficiencies, (described in section 2.1.1.4 and 2.2.2, pointed out by Miller (1984)).

2. Sumanth (1979) defined Total Productivity as the ratio of total tangible

output to the sum of all the tangible inputs, as mentioned in Table 2.1 of section

2.1.2.1. Hence, his Productivity-Profit model initially considered "all the inherently

measurable inputs and outputs" (p. 6.3), either in physical terms or in terms of value.

However, as modified later in 1994 by himself, "the tangible output and tangible

input have to be expressed in value terms because all the output and input elements

are not in the same units" (p. 154). His idea is exactly the same as explained in the

first point of this section.

In addition, Sumanth's model has a significant limitation. That is, only the

total tangible output is assumed constant can the negative linear relationship exist

(see section 2.2.2.3). This assumption may be reasonable for a short period of time;

however, from a long-term standpoint, it may not be appropriate. Therefore,

Sumanth's model may not be applicable in the long term.

3. Miller's first model stresses the use of dollars as the unit of measure of

both profitability, productivity, and price recovery. Thus, his model demonstrates

that profitability equals the sum ofproductivity and price recovery, not the product of

productivity and price recovery as expressed by the Adam-Hershauer-Ruch's model

or APC's model.

88

It is unusual that this model expresses both profitability and productivity in

terms of dollars. Since the definitions ofproductivity and profitability examined in

section 2.1.2.1 (Table 2.1) and section 2.1.2.3 (Table 2.3), all show that these two

terms are ratios, the units of measure in the Miller's first model are apparently

different from others and are not easily accepted.

Miller's second model, the Productivity-ROI model, also has the same units of

measure as defined in his first model. He measures the profitability change Pt

(equation [2-28]), and productivity component (the two terms in the first bracket of

equation [2-32]) both in terms of dollars. This also results in the same problem: the

definitions ofproductivity and profitability differ significantly fi-om those generally

accepted.

4. Papadimitriou (1992) explained the Productivity-Profit relationship by the

decomposition approach. He related productivity with the growth of profit.

However, he did not clearly define profitability and the growth of profit. There was

no clear distinction between these two terms.

Based on the above discussion, no current model is perfect. This is to be

expected the models do not have a common definition ofproductivity. Because of

the variety of manufacturing environments, an applicable model must have its own

definitions to develop.

89

2.3.3 Deficiencies and Limitations of Current Quality-Productivity Models

In this section, the deficiencies and limitations ofthe five models presented in

section 2.2.3 are addressed.

1. In Deming's model, he did not give definitions for quality and productivity.

As Deming (1986) stated that "Quality can be defined only in terms ofthe agent" (p.

168), he thought quality had different meanings to different levels of employees.

Deming developed his model to stress his viewpoints that focusing on quality

improvement could lead the productivity improvement. However, because of a lack

of definitions, the relationship between quality and productivity becomes

questionable.

2. Thor's model regards quality and productivity essentially as the same thing.

However, if quality and productivity were the same, then there is no need to discuss

the relationship between them. Since the original meaning of "productivity" is not

used as an another form of "quality," one needs to be carefiil when interpreting the

relationship between these two terms. Quality and productivity are closely related;

however, the degree of relationship may vary in different departments or functions.

Therefore, it is not appropriate to assert that these two terms are synonymous in every

situation.

3. In Adam-Hershauer-Ruch model, the relationship between quality and

productivity from the standpoint ofthe cost unit is considered. Thus, Sumanth (1994)

called it the cost unit approach. He mentions three points to consider on this model:

90

a. The Quality-productivity ratio might be a misleading measure

when the unit processing cost and the unit reject-correction cost

depend on the number of rejected items.

b. The estimated cost based on the historical data might not reflect

the current cost.

c. This model did not show whether or not the rejected goods are

repaired and become acceptable in the same period.

In addition to Sumanth's comments, there are four more issues to be

addressed:

a. It is not clear whether the rejected goods are from the customer's

standpoint or from the standpoint of supplier's quality personnel. Unless

100% inspected, there exists a risk in acceptance sampling between

customer and supplier. Besides, due to the potential difference in the

recognition on product quality, the goods that supplier values may be

determined as rejected by the customer. It will cause some trouble in

determining the number of items not rejected in this model.

b. It does not consider the items not finished. Usually, a specific period of

time is a common base for the calculation of this model; however, during

this time period, it is very likely that some items are not completely

91

finished, i.e., some items remained in work-in-process condition. This

model does not explain how to deal with these work-in-process items,

c. If the unit reject processing cost significantly decreases as the number of

rejected items increases, the QPR may increases even though the percent

defective of items increases. Two cases in Table 2.4 can be used to explain

this fact. Case I is the example used by Adam, Hershauer, and Ruch for

explaining the calculation of QPR. The data of total number of items, unit

processing cost, number of rejected items, and unit reject processing cost in

Case I are given. The QPR value is obtained from equation 2.34. Case 2

assumes that the number of rejected items doubles while the total number

of items and its unit processing cost remain unchanged. The unit reject

processing cost decreases significantly because ofthe increasing number of

rejected items. The QPR increases from 4.5 in case I to 5.0 in case 2. It

demonstrates that the QPR increases, but the percent of good items

decrease. It is easy to understand that the product quality increases while

the number of rejected items is cut in half

Table 2.4 Comparison of QPR Values When Unit Reject Processing Cost Significantly Decreases

Case I

Case 2

Total number of items Nimiber

100

100

Unit processing cost

$0.1

$0.1

Rejected items Number

10

20

Unit rejected processing cost

$1.0

$0.3

QPR

4.5

5.0

92

4. Edosomwan's model considers the quality-productivity relationship from a

broader viewpoint. It presents not only the improvement approach of management,

but also the statistical method in relating the quality-productivity relationship. It is a

more thorough and detailed model than any other. However, it is also necessary to

note some points:

a. The (Pj, Q\) data can be either assigned rank data or measured

quantitative data. Assigned rank data are used for calculating the

rank correlation coefficient RC{C{. RCjCj is used in the PAQAM,

which is a matrix with the ranks of quality and productivity as its

axes. Measured quantitative data are used for calculating the

sample correlation coefficient SCjCj. SCjCj formula assumes

bivariate normal population for paired data {?{, Q[). However,

there is no connection between RCjCj and SCjCi.

b. Sample correlation coefficient SCjC^ expresses the extent and

direction that quality and productivity are correlated. It can also tell

how much variation of one variable is caused by the other variable

based on the coefficient of determination SCjC^ j . However, it

cannot indicate which is the cause and which is the effect. To

discern cause and effect is an important measure for management.

5. Sumanth and Wardhana's QPP model was developed based on Sumanth's

(1979) Total Productivity model and Dawes' model. Therefore, the deficiencies and

93

limitations of these two models mentioned previously still apply to Sumanth and

Wardhana's QPP model. That is:

a. Sumanth and Wardhana's QPP model also employs the quality costs

concept to measure the costs other than working capital.

b. The Sumanth and Wardhana's QPP model may not be applicable for

long-term purposes.

In addition, Sumanth and Wardhana's QPP model also has the following

deficiencies and limitations:

c. This model is used only for quality in terms of level of conformance

( % ) .

d. It is difficult to directly determine the relationship between quality.

Total Productivity, and profit from the two-dimensional Figure 2.13.

e. Based on Figure 2.13, it seems that the quality conformance level at the

break-even-point is always at Q2 = 50% or so. However, this is not

true. As Sumanth and Wardhana described, the quality conformance

level at the break-even-point should at the point where the input costs

other than working capital (F) equals the tangible output at the base

period.

94

2.4 Research Agenda

In this section, definitions regarding the research problem will first be given.

The conceptual model of this research is also presented. These definitions and

conceptual model comprise the basic framework for this research.

2.4.1 Definitions of This Research

Before starting research, it is necessary to clarify the terms used. The

following subsections define and explain the basic terms used in this research:

quality, productivity, profit.

2.4.1.1 Definition of Quality

The term "quality" used in this research refers to the "product quality," or "lot

quality." Product quality is defined as the conformance level ofthe characteristic(s)

of a product that meets customer's specification(s). The point at which the

conformance level just meets the customer's specifications for a product is called the

minimum acceptable product quality.

Because the conformance level can be explained either in terms of individual

product or in terms of lot, product quality as defined above is apparently in terms of

individual product. If a lot conformance level is required, it is called lot quality. Lot

quality is defined as the conformance level at which a lot satisfies the customer

requirement. Similarly, the point at which the conformance level just meets the

95

customer's specified requirement for a lot is called the minimum acceptable lot

quality.

Lot quality is usually specified when 100% inspection is impossible (e.g.,

destructive inspection) or uneconomical. In such situations, sampling inspection is

the only choice. However, because ofthe sampling risk, the customer must allow for

a defined level of defective product.

For example, if ten thousand fluorescent lamps are ordered, it is impossible to

test the product characteristic, (e.g., lighting duration for 1000 hours), for all ten

thousand lamps. In this case, sampling inspection is inevitably applied and a lot

quality (e.g., 99.5% ofthe ten thousand lamps exceed the duration 1000 hours) must

be specified. The minimum acceptable lot quality is 99.5% in this case.

2.4.1.2 Definition of Productivity

In this research, productivity is defined as the profit-based ratio of valuable

output to measurable input during a specified period. The term "valuable outpuf

means that the output has a market value. Also, "measurable input" refers to all the

input that can be measured by or transferred into dollars. Therefore, the unit of

measure for productivity used in this research is dollars to dollars, and productivity is

profit-based.

Because ofthe influence of inflation or deflation, the same amount of dollars

has different values at different times. Since the output always lags behind the input.

96

it is necessary to take into account the inflation or deflation factors. For the purpose

of measuring the productivity of a product, three assumptions are needed here. First,

the time lags between the output and input ofthe same product are assumed constant.

Second, the influence ofthe time lags among input costs are negligible. That is, the

input costs incurred at different time points within a short period of time are assumed

having no deflation of inflation. Third, the influence ofthe time lags among the

outputs sold are negligible. That is, the output (resulted from the same input) values

produced at different time are assumed having no deflation or inflation.

Because the object of this research focuses on manufacturing companies,

valuable output refers to the products that are to be sold to customers, either external

or internal customers. "External customers" are the customers who directly purchase

the products outside the manufacturing company.' "Internal customer" refers to the

other divisions, departments, etc. that are users of valuable products in the same

manufacturing company. On the other hand, input is usually viewed as synonymous

with total cost in the manufacturing environment.

' This definition differs fi-om Juran and Gryna's (1993) definition. They explain the external customers as both ultimate and intermediate users, including government regulatory bodies.

' This definition also diflfers fi-om Juran and (jiyna's (1993) definition. In their explanation, internal customers include all the divisions provided with or affected by components or subassemblies. According to Juran and Gryna, a Purchasing Department is an internal customer because it receives the specifications for procurement. However, a Purchasing Department is not regarded as an internal customer in this research unless it is also a user ofthe manufactured products.

97

In addition, productivity, as defined above, implies the Total Productivity

only. Total Productivity, as defined by Sumanth (1994), is a ratio of total tangible

output to total tangible input. It is a ratio measuring the overall productivity.

2.4.1.3 Definition of Profit

In this research, profit is used as the base to link productivity and quality.

Profit is defined as the difference between revenue and cost.

In addition to the definition, there are three points that need to be noted:

1. In this research, profit refers to the gross profit before tax.

Since different tax rates influence the net profit, and hence may change the

relationships among quality, productivity, and profit, only the profit before

tax is considered.

2. All profits, revenues, and costs are measured in the base-period equivalent

value.

The purpose of this requirement is to rule out the impact caused by

inflation or deflation in the relationship models.

3. Profit comes mainly from the sales of product.

In order to avoid misconstruing the relationships among quality,

productivity, and profit, profits that are not from the sales of product are

not considered in this research.

98

2.4.1.4 Definition of Cost

Cost and profit are closely related. Although in this research, the Quality-

Productivity relationship is developed based on profit, it does relate to the calculation

of cost. Therefore, cost must also be defined for this research.

Except where specified, cost in this research is defined as the production cost.

Since this research focuses on the quality-productivity relationship, the costs incurred

in the production activities are the main concern. The marketing costs and

administrative costs are not included in the production cost.

Production costs include the direct material, direct labor, and factory

overhead incurred to produce a product. Direct material cost is the cost of any raw

material that becomes an identifiable part ofthe finished product. Direct labor cost is

the wage earned by a worker who transforms the state of material or part to another

state, e.g., finished product. Factory overhead includes all production costs other

than direct material and direct labor. Since cost is referred to production cost, factory

overhead is simply called overhead in this research.

Both profit and cost are measured in terms of US dollars in the base period.

Profit and cost in the confirmatory study are converted from Taiwaness currency

values into the equivalent US dollars based on a fixed exchange rate.

99

2.4.2 Conceptual And Mathematical Models

In this section, three conceptual models are presented: Quality-Profit Model,

Productivity-Profit Model, and Quality-Productivity Model. The mathematical

models, developed in Appendix A, for these three relationships are also presented

along with the conceptual models. In addition, a conceptual model describing the

approach for linking quality and productivity is also presented.

2.4.2.1 Relationships among Quality, Price. Revenue. Volume Sold, and Costs

2.4.2.1.1 Price-Volume-Quality Relationship

Since quality is defined as the customer-oriented product quality in this

research, it is believed that the improved quality will result in more profit. The basic

relationship between the selling price, volume sold, and the quality of conformance is

illustrated by Figure 2.15. This figure shows, that at a fixed price, the higher the

quality of conformance, more volume is sold. Buzzell and Bradley (1987) stress that

the PIMS (Profit Impact of Market Strategies) study has shown that higher quality

results in higher market share.

2.4.2.1.2 Revenue-Quality Relationship

Since revenue is considered mainly from the sale of products. Figure 2.15 can

also be expressed in terms of revenue (see Figure 2.16). Figure 2.16 illustrates that

the higher the quality of conformance, the more significant the revenue increases.

100

.S ^^

Q,: The lower quality level of conformance

Qj: The higher quality level of conformance

Volume sold (V)

Figure 2.15 Price-Volume-Quality Relationship

i

o s s V > « X

L

0 % Qi Q2

Quality of conformance

i k

100%

Figure 2.16 Revenue-Quality Relationship

101

2.4.2.1.3 Cost-Volume-Quality Relationship

Total production costs will eventually be reduced when quality of

conformance increases. The relationship between production costs, volume sold, and

quality is illustrated in Figure 2.17. This figure also shows, that at a fixed production

cost, the higher the quality of conformance, the lower the required volume sold.

i

(J)

Cos

ts

Prod

ucti

on

k

Q2

Q,: The lower quality of conformance

Q^: The higher quality of conformance

Q,

Volume sold (V)

Figure 2.17 Production Cost-Volume-Quality Relationship

2.4.2.1.4 Cost-Quality Relationship

Figure 2.17 can be expressed in terms of costs and quality of conformance as

shown in Figure 2.18.

102

o U e o

'•5

3

0

CL

0% Q i Q.

100%

Quality of conformance

Figure 2.18 Production Cost-Quality Relationship

2.4.2.2 Quality-Profit Model

The conceptual model for Quality-Profit, expressed in Figure 2.19, is

developed primarily from the Figures 2.16 and 2.18. Equation [2-44] through [2-46]

express the mathematical model of Quality-Profit relationship. This model

development, which is based on the concept of ranks, is listed in Appendix A 18

r(Pu) = ai + bir(Q) [2-44]

•' Equations [2-44] = [A-8], [2-45] = [A-12], [2-46] = [A-13]

103

Zr(Q,)r(P^.)-n(n+l)'/4 bi = ^ V - [2-45]

Z[r(Q.)]'-n(n +1)^/4 i = l

ai = (l-bi)(n+l)/2 [2-46]

where

Pu: Unit Profit

Q: Quality conformance level (%)

r(Pu,): the ith rank of Pu in an ascending Pu series

r(Q,): the ith rank of Q in an ascending Q series

n: number of paired data.

Figure 2.19 depicts that the break-even point ofthe quality of conformance is

located at the point where the unit revenue is equal to the unit total input.

104

Vi

B 'o O

0 Quality Level ofConformance 100%

Unit Profit

Figure 2.19 Quality-Profit Relationship

2.4.2.3 Productivity-Profit Model

The conceptual model for Productivity-Profit is expressed in Figure 2.20. It

shows that when productivity equals one, neither profit is obtained nor losses are

incurred. The mathematical model is shown in the equation [2-47]. Its model

development is seen in Appendix A. 19

19 Equation [2-47] = [A-2].

105

Pu = (P-l)x:|^ [2-47]

where

Pu: Unit Profit

P : Productivity

I : Total input

V: Production volume.

o D

olla

rs

0

/

/

Unit Total Input

/ 1

/

*^

Unit Profit

Unit Revenue \

oc

Productivity

Figure 2.20 Productivity-Profit Relationship

2.4.2.4 Quality-Productivity Model

Figure 2-21 shows the conceptual model for the Quality-Productivity

relationship. As quality improves, unit profit increases. Similarly, as productivity is

106

enhanced, unit profit also increases. Hence, quality and productivity go hand-in-

hand. Equations [2-48] through [2-50] exhibit the mathematical model for Quality-

Productivity relationship. This model development is also listed in Appendix A

This model is also developed based on ranks.

20

C30

O

O

&a

P=l

Q=o

-oo

P X ^ BEP /

Pr A

of rej

it; ; I M :

100

jr \ Quality Loss >^ o /f»/ X ^ BEP (% Area yr

)

Figure 2.21 Quality-Productivity Relationship

20 Equations [2-48] = [A-23], [2-49] = [A-24], [2-50] = [A-25].

107

r(P) = a2 + b2r(Q) [2-48]

n

Zr(Q.)r(P.)-n(n + l )^ /4 b2 = —^ [2-49]

Z[ r (Q. ) ] ' -n (n +1)^/4 i= l

a2 = (l-b2)(n+l)/2 [2-50]

where

P : Productivity


r(Pi): the ith rank of P in an ascending P series

r(Q,): the ith rank of Q in an ascending Q series

n: number of paired data of (Q, P).

2.4.2.5 Conceptual Model of Linking Productivity and Quality in Confirmatory Study

The conceptual model of linking quality and productivity used for

confirmatory study in industries is presented in Figure 2.22. In this Figure, customers

determine the product and its quality. All input factors are prepared for

manufacturing such product. Through the unit profit, a Quality-Productivity

relationship is linked. In this research, total input is regarded as synonymous with the

total production cost.

108

^ r

Quality — •

V

Customer

T V

Measurable Input Factors

n

Revenue ^ ^ t Gross from ,_ „ Total p^fi t ^

Selling / P ^ ^ - ^ - )-l 1 , Products Costs ^J^^^^^^,

I Direct \i Direct W Over- \ Labor ,' Material A head^' j

h

i Quality-

Productivity Relationship

—^

^ r 1

Productivity

^ '

Figure 2.22 Conceptual Model of Linking Quality and Productivity '

2.4.2.6 The Comparison between the Proposed Model of This Research and Sumanth and Wardhanas' Model

Both the proposed model of this research and Sumanth and Wardhanas'

(1993) model are to explore the relationship between quality and productivity based

on profit. However, since Sumanth and Wardhanas' model has major drawbacks, the

' Although the Activity-Based Cost accounting may provide more accurate information than the overhead method, it is seldom utilized in Taiwan's manufacturing industries. The cost data of this research were collected according to the costing systems the investigated companies currently use.

109

proposed model of this research is more appropriate to explain the profit-based

Quality-Productivity relationship. The three major drawbacks of Sumanth and

Wardhanas' model are described in the following.

1. The term "cost" used in Sumanth and Wardhanas' model is not congruent.

Sumanth and Wardhanas' model was developed by combining two models,

Dawes' model of quality of conformance and Sumanth's Total Productivity Model

(TPM). The cost used in Dawes' model was the "quality cost," while in Sumanth's

TPM was the "input cost." The term "quality cost" is not equivalent to "input cost,"

neither in concept nor in mathematics. Hence, the quality-productivity model

resulting fi-om combining these two models based on different cost bases is

questionable.

2. The relationship between profit and costs in Sumanth and Wardhanas'

model is not clear.

This drawback relates to the first drawback. Since profit is gained by

subtracting the costs, and costs are explained in two different ways in Sumanth and

Wardhanas' model, the calculation of profit is also questionable. Qriginally, in

Sumanth's TPM, profit is linearly related to input cost. However, in their final

model, profit is calculated by comparing with quality costs. This would result in a

question as to the meaning of what profit stands for in their model.

3. The cost category in Sumanth and Wardhanas' model may not be

applicable to all industries.

110

In Sumanth and Wardhanas' model, the input costs are primarily classified

into human, material, capital, energy, and other expense. This classification is

originally designed for calculating partial productivity. However, this classification

may not be adopted by industries in calculating the product costs.

The proposed mathematical models of this research overcomes the major

drawbacks in Sumanth and Wardhanas' model. Compared with the Sumanth and

Wardhanas' model, these proposed models have the following major merits:

1. Production cost is more practically used than quality cost.

Quality cost is an excellent concept in quality management; however, it is

seldom employed in the cost accoimting system in the real world. This is

because quality cost does not equal production cost. Under the most

current accounting system, production cost is a better measure because it

directly affects profit. So far, there is no accurate and detailed criteria to

calculate quality costs for general purpose. From the practical view points,

production cost is more likely to be calculated and applied.

2. Profit and revenue are clearly defined in the proposed models

In addition to the income from selling products, there are many other

sources of revenue. For instance, investment income or gains on disposal

of fixed assets are not imusual in a company. These non-operating revenue

also affect profit; however, they apparently have nothing to do with the

productivity or product quality. The proposed models of this research

111

concentrates on the revenue from selling products. In addition, profit is

defined as the before-tax gross profit and is simply obtained by subtracting

total cost from total revenue.

3. Instead of directly measuring the Quality-Productivity relationship by using

ratio scale or interval scale of measurements, it is more appropriate to

measure it with ordinal scale of measurement.^^

Quality, as well as productivity, can be defined in hundreds of ways. For

example, number of defects per 100 pieces or one lot, or per 1000 yards,

etc. Only when these data are converted to conformance level % can they

be used to relate to other variables. These transformed data are not the

data of ratio scale. It is questionable that Sumanth and Wardhanas' model

uses these potential ordinal data to establish their formula. The proposed

models, especially Quality-Profit and Quality-Productivity models, utilize

the concept of ranks to compare the relationships between variables. This

approach does not necessarily need interval or ratio data, ordinal data is

enough for the analysis.

^ According to Conover (1980), an ordinal scale of measurement "refers to measurements where only the comparisons 'greater,' 'less,' or 'equal' between measurements are relevant." The interval scale of measurement considers "not only the relative order ofthe measurements as in the ordinal scale but also the size ofthe interval between two measurements." In addition to the order and interval size, a ratio scale of measurement must also have a meaningful ratio between two measurements. The distinction between the ratio scale and the interval scale is that the ratio scale has a natural zero measurement, while the zero measurement of interval scale is defined arbitrarily.

112

2.4.2.7 Advantages of Relating Quality-Profit and Quality-Productivity Models Based on Ranks

Because ofthe deficiencies and limitations of current mathematical models

addressed in sections 2.3 and 2.4.2.6, this research proposed the Quality-Profit and

Quality-Productivity models based on ranks. The reasons, also the advantages, for

using the concept of ranks for developing models of this research are:

1. Models based on ranks are more generalizable.

Different manufacturing environments have their own features, except

for the use ranks, it is hard to find a unique model to relate quality, profit,

and productivity for all cases.

2. Models based on ranks are more reliable.

Data used in the models based on ranks do not need accurate as the original

data. Therefore, ranks may reduce the effects caused by original data bias

or errors.

3. Models based on ranks can be applied to various definitions of quality,

productivity, and profit.

By using ranks, the problem of different definitions for variables can be

eliminated in a model based on ranks.

4. Models based on ranks can avoid the problem of misusing measurement

scales.

When quality can only be measured using an ordinal measurement scale, it

is unreasonable to relate the quality data to a model based on interval or

113

ratio scales of measurement. However, by using ranking, this type of

quality data can be utilized in a model based on ranks.

2.4.2.8 Contributions of This Research

The contributions of this research are addressed from both theoretical and

practical standpoints. The theoretical contributions of this research lie mainly in the

development of proposed mathematical model. Specifically, there are three points

viewed as contributions in theory.

1. The proposed model is the first model to use nonparametric statistical

approach to establish the mathematical models for Quality-Profit and

Quality-Productivity relationships.

2. The positive relationships of Quality-Profit, Productivity-Profit, and

Quality-Productivity are proved through the proposed mathematical

models.

3. The proposed model is the first one to utilize the concept of unit profit to

compare with Quality, Productivity, and be a base for relating Quality-

Productivity and to establish models for them. Unit profit is more

meaningful because total profit is tremendously affected by sales quantity.

The practical contributions of this research are:

1. The proposed model is the first model used for a confirmatory study on the

Quality-Productivity relationship in manufacturing companies.

114

2. Through the field study, the positive relationship between quality and

productivity are confirmed and validated by this research.

115

CHAPTER 3

RESEARCH METHODOLQGY

Research methodology is a way of solving problems (Leedy, 1993).

Therefore, the research process is first addressed to describe the way this study

proceeds. Following this research process, methodological issues regarding research

design, data collection and treatment, measurements, and constraints are presented.

3.1 Research Process

Research process describes the steps a study follows. Figure 3.1 illustrates the

research process of this study which are discussed in the following.

1. Research statement

The research statement, delineated in Chapter 1, illustrates the outline

of this research, including the following: problem statement, scope of

research, limitations and assumptions, research needs and benefits, and

expected results.

2. Literature review and models

This step was covered in Chapter 2 which stems from the literature

review and follows the conceptual models and mathematical models.

3. Research design

The research design is discussed in section 3.2.

116

•.Problem statement |. Scope of research :..research question : ..research purpose j ..research objective : ..general hypothesis

•.Literature review • ..history :.. definitions '..current models •..deficiencies & : limitations of •

: current models

.Type of research •.Research focus ;. Research hypothesis I Research ; environment

j.Data collection :..data attributes •..data location •..data access j.Data treatment :.. data re view '..data conversion

iData analysis .regression analysis .hypotheses test .statistical inference:

:. Conclusions ^.resuh •

•..constraints i.apphcability

Research statement

Research limitations & assimiptions Research needs and benefits Expected results

Literature review & conceptual model

^Conceptual "mocfels' •.definitions LMathematical models:

^ r

Research design

>

iResearch method : • I

vResearch instrument '• 1 t

Data collection & treatment

•.Measiirement • ..rehabiUty :.. validity i.repUcability •..bias

Data analysis & interpretation

•.Data interpretation : ..theoretical : interpretation :..practical : interpretation

Conclusions & recommendations

iRecommendations :..theoretical •

[..practical

Figure 3.1 Research Process of This Study

117

4. Data collection and treatment

The methodology of data collection and treatment are addressed in

the section 3.3 of this chapter. Issues regarding data measurement,

reliability, validity, replicability, bias, and representativeness are discussed

in Section 3.4. In addition, some research constraints are presented in the

last section of this chapter.

5. Data analysis and interpretation

This step is conducted after data is collected. The statistical

approach is the primary tool in data analysis. Results of data analysis

are interpreted theoretically and practically.

6. Conclusions and recommendations

The last step of this research is to summarize the results and draw

conclusions. Suggestions for fiulher research may be made based on the

results of this study.

The research process constructs the framework of this research. The following

chapters and sections proceed according to this framework.

3.2 Research Design

The purpose of research design is to provide a plan for research. In this

section, the following issues are addressed: type of research, research focus, research

hypotheses, research environment, research method, and research instrument.

118

3.2.1 Type of Research

This research is basically classified as quantitative. Because it investigates

the relationship between quality and productivity based on profit, much numerical

data are required to develop and verify the relationship.

This research can also be classified as an empirical confirmatory study. Two

cases studies were conducted in Taiwan's industries to confirm the positive

relationship between quality and productivity. In addition, because a practical

solution is sought for manufacturing systems, this research may also be considered

applied research.

Because this research is to conduct a confirmatory study, its research logic is

essentially deductive. However, during the research process, the mathematical

models developed for each relationship among quality, productivity, and profit

require inductive logic to lead to a specific model. Therefore, although the overall

research is deductive, the logic of model development is inductive. Thus, it can be

stated that this research is a quantitative-deductive-applied-confirmatory research

project.

3.2.2 Research Focus

This research focuses mainly on three issues as follows:

I. Study the relationship between product quality and unit profit for

manufacturing products.

119

2. Study the relationship between productivity and unit profit for


3. Study the quality-productivity relationship based on unit profit for


The definitions of quality and productivity used in this research are presented

in sections 2.4.1.1 and 2.4.1.2. Profit used for comparing and relating with variables

is unit profit, which is an average profit per product.

In addition to the above issues, the following secondary issues closely related

to the main issues are also investigated:

1. Whether the proposed Quality-Profit relationship model is applicable in a

manufacturing system.

2. Whether the proposed Productivity-Profit relationship model is applicable

in a manufacturing system.

3. Whether the proposed Quality-Productivity relationship model is applicable

in a manufacturing system.

3.2.3 Research Hypotheses

This research has a main hypotheses and two sub-hypotheses. Figure 3.2

states the main hypotheses and Figure 3.3 states the sub-hypotheses. Both main

hypotheses and sub-hypotheses are tested. The purpose of these hypotheses tests is to

verify the relationships identified in the mathematical models.

120

Main Hypotheses

In a manufacturing company, the productivity levels of a product have a

probability distribution that is positively dependent ofthe levels of product

quality of conformance of that product.

That is, if Qi denotes the conformance level at time i of a product and P,

represents the productivity level resulting from Qi at time i, and if

Qj >Qj , foranyi, j =1 , 2, ..., n, i^j,

then, the null and alternative hypotheses are

H„: P; ^ P,

H,:P, >P,

respectively.

Figure 3.2 Main Hypotheses of This Research

121

Sub-hypothesis 1

The profit of a manufacturing company has a probability distribution that is

positively dependent ofthe levels of product quality of conformance.

That is, if Q, denotes the quality conformance level at time i of a product

and Pu, represents the unit profit resulting from Q, at time i, and if

Qi >Qj , foranyi,j =1 , 2, ..., n, i;«tj,

then, the null and alternative hypothesis are

H„: Pu; ^ Pu,

H,: Pu, > Pu,

respectively.

Sub-hypothesis 2

The profit of a manufacturing company has a probability distribution that is

positively dependent ofthe productivity levels ofthe product.

That is, if P, denotes the productivity level at time i of a product and Pu,

represents the unit profit resulting from P, at time i, and if

Pi >Pj, foranyi, j =1 , 2, ..., n, i^],

then, the null and alternative hypotheses are

HQ- Pui - Puj

Hp Pu, > Puj

respectively.

Figure 3.3 Sub-Hypotheses of This Research

122

3.2.4 Research Environment

This confirmatory study were conducted at two companies in Taiwan.

Because the companies requested to remain anonymous, their names were replaced

by ABC Company and XYZ Company, respectively, throughout this research. Both

companies were invested in by Taiwan entrepreneurs. The ABC Company was

typically a traditional industrial company. The XYZ Company represented a newly

developing industry in Taiwan. The following two subsections present a brief

overview for each company.

3.2.4.1 ABC Company

ABC Company, at the time ofthe study, was one ofthe leading companies in

Taiwan's textile industry. The capitalization of ABC Company in 1995 was 120

million equivalent US dollars. The textile revenue in 1995 was an estimated 113

million US dollars, accounting for about 83 % ofthe company's total operating

revenue. This company had eight factories scattered in northern and central Taiwan.

Each factory was engaged in different processes of products. Due to time and cost

constraints, three factories which were located closely in northern Taiwan were

selected for study.

The factory produced five products: gingham, piece-dyed fabric, chambray,

denim, and printed flannel. The main customers of these products were from the

USA, Southeast Asia, and Hong Kong. Among the products, gingham and piece-dyed

123

fabric were the two chief products and were selected for this research. The

production process of gingham is illustrated in Figure 3.4. The process of piece-dyed

fabric was very similar to that of gingham except dyeing was processed after sizing.

Cotton

^'

Dyemg

r r ^

Drawing

r ^ Combmg

Warpmg

Weaving

W

Spinning

Sizing

Finishing

I J Figure 3.4 The Production Process of Gingham in the ABC Company

The selected three factories were named A, B, and C, respectively. Factory A

basically processed spinning and dyeing. Factory B dealt with warping and sizing.

Factory C also processed dyeing and sizing. Each factory had from 80 to 120

employees, which were divided into three shifts. The management style was close to

Japanese style and highly emphasized quality. Since labor cost accounted for a large

portion of production cost, labor productivity was measured for evaluating

effectiveness and efficiency.

124

3.2.4.2 XYZ Company

XYZ Company, at the time ofthe study, was a manufacturer of network

products in Taiwan. It was established in 1989 in northern Taiwan. The

capitalization of XYZ Company in 1996 was US$ 13.1 million. This company had

nearly 80 employees and the sales revenue was US$ 7.8 million in 1995.

The major products of XYZ Company were Token Ring, Ethernet, Remote

Access, SOHO (Small Office, Home Office) Network, Wireless LAN (Local Area

Network). Most ofthe customers were scattered around the world, especially the

developed countries. In America, the US Air Force, JC Penny's, Chemical Bank,

GTE, and Chevron were their major customers.

In its business activities, the XYZ Company had engaged in partnerships with

industry leaders and customers. Among XYZ's partnerships were its relationships

with Token Ring industry leader, IBM, and Ethernet industry leader, Novell. These

industry partnerships had led the XYZ Company to develop easier to use and install

products.

The XYZ Company emphasized R&D as well as production. However,

design was usually the most critical problem in this company. In order to meet fast

development in PC network applications, the XYZ Company employed nearly one

third of its employees in R&D. More than half of these R&D engineers possess

master degrees in Electronic or Control Engineering. The production department

also had more than one third ofthe employees. Product quality must be 100%

125

guaranteed after products are shipped to customers, so management highly

emphasized quality issues.

Among the major products, PNP (Plug and Play) Ethernet Combo and Token

Ring 16 Bit ISA IBM were the two products the XYZ Company focuses on mostly

since the second quarter of 1996. The production processes of these two products

were basically the same. The difference lay primarily in the design, which did not

affect production process much. Figure 3.5 illustrates this production process.

( \ Raw materials

(parts)

•y r

Bum-In

^ r r ^ IPQC (In-Process Quality Control)

\ r

^ FQC ^ (Final Quality

Control)

r SMT ^ (Surface Mounting

k Techniques) j

^ IQC ^ (Incoming

, Quality Control),

r > Functional

Test I

( \ Software Copying

^ J

Storage

r ^ Functional

Test II

Packaging

Figure 3.5 The Production Process of PNP Ethernet Combo in XYZ Company

126

3.2.5 Research Method

The method used by this research in the selected companies is depicted by

Figure 3.6. The task force in each company assisted the research by participating

discussion for definitions, terms, supporting required data, reviewing collected data,

and providing other services, such as process and product introduction, and

professional opinions. Statistical analysis, including hypotheses testing and

regression analysis, was done by the researcher. Model verification and

interpretation for the results were completed after the statistical analysis.

3.2.6 Research Instrument

The instruments used in this research are as follows:

1. Statistical tool: Regression analysis in Excel 5.0, nonparametric statistical

program from Dr. W J. Conover.

2. Personal computer (CPU 486DX2-66) and associated software (VISIO 4.0,

WORD 6.0).

3.2.7 Measurement of Costs and Profit

Profit is a key variable in this research. It is used for linking with Quality and

Productivity respectively. As defined in section 2.4.1.3, profit is obtained by

subtracting production cost from revenue in this research. Hence, it is necessary to

describe the measurement of costs and profit. The measurement of production costs

127

r

• ^

Modeling

Interpretation

r Model

Verification

Data Collection

Hypotheses Test

Regression Analysis

Figure 3.6 Research Method in the Field Study

in industries is consistent with the theory of cost accounting and is adopted by this

research. Profit is totally created from revenue; therefore, revenue is also explained

within the discussion of measurement of profit.

128

3.2.7.1 Measurement of Costs

As addressed in section 2.4.1.4, cost is referred to production cost and is

classified into direct material, direct labor, and overhead in this research. The

problem in measuring production cost lies primarily in the allocation of overhead.

The base of overhead allocation must be first considered. Although there are several

bases, such as direct labor hour or direct labor cost, etc., it must be recognized that no

unique base is perfect for all industries.

The bases of allocating overhead in this research were depended upon the

allocation system currently used by the companies. In other cases, the bases may be

determined according to the following:

1. Cost unit base— if the unit cost of each product is known.

2. Volume base— if products and their manufacturing processes are similar.

3. Direct material base-- if direct material cost is higher than direct labor cost.

4. Direct labor base- if direct labor cost is higher than direct material cost.

5. Machine hour base-- if machine hours of manufacturing products are

Known.

3.2.7.2 Measurement of Profit

As defined in section 2.4.1.3, profit is the difference between revenue and

production cost. If the cost is known, then profit is determined by revenue, which is

the product of selling price times sales quantity. Selling price is determined by the

129

company and market/customer. Sales quantity is measured per order or lot.

Therefore, profit is measured by an order or a lot. However, because it is most likely

that the product quantity in each lot or order varies, it is necessary to use the unit

profit (profit per piece) as the base in comparing with quality or productivity.

In order to avoid misconstruing the quality-productivity relationship by other

unrelated factors, the revenue in this research is totally from the sale of products.

Other income not directly from the sale of products, such as the disposal on fixed

assets or the investment income, are not considered revenue in this research.

3.2.8 Test plans of This Research

According to the hypotheses of this research presented in subsection 3.2.3,

three test plans must be established. Figures 3.7, 3.8, and 3.59 illustrate the test plans

for Quality-Profit, Productivity-Profit, and Quality-Productivity relationships

respectively.

3.2.9 Specific Models Establishment

In addition to confirm the relationships among quality, productivity, and

profit, the specific models, Eqs. [3-1] through [3-7], for the investigated products and

companies were also established. These models would help the company realize how

these performance measures, quality, productivity and unit profit relate to each other.

130

1. Test hypotheses: If Q,>Q^, foranyi,j =1, 2, . . . ,n, i 9 j , then

H,:Pu. > Pu,

2. Test data & description:

Product: Location:

Order (Lot) # Prod. Quantity Quality (%) Revenue Production Cost Profit @Profit Other

3. Normality test: (Figure & analysis)

4. Statistical test: (a = 0.05)

5. Conclusion:

Figure 3.7 Test Plan for Quality-Profit Relationship

131

1. Test hypotheses: If p. >P^, foranyi,j =1, 2, . . . ,n, i7ej,then

Ho: Pui ^ Puj

H,: Pu. > Pu,


Product: Location:

Order (Lot) # Prod. Ouantity Revenue Production Cost Profit @Profit Productivity Other



5. Conclusion:

Figure 3.8 Test Plan for Productivity-Profit Relationship

132

1. Test hypotheses: If P| >Pj, foranyi, j =1, 2, . . . ,n, i?tj,then

Ho: Pu, ^ Puj H,:Pui>Puj


Product: Location:

Order (Lot) # Prod. Ouantity Oualitv (%) Revenue Production Cost Profit (giProfit Productivity



5. Conclusion:

Figure 3.9 Test Plan for Quality-Productivity Relationship

133

The establishment ofthe specific models are illustrated as follows:

I. Quality-Profit model

Let Q, denote the quality conformance level of ith lot

Pu, denote the unit profit of ith lot

r(Qi): the ith rank in the ascending Q series

r(Pu,): the ith rank in the ascending Pu series.

Then, the model is

r(Pu) = ai + b,r(Q) [3-1]

where

n

Zr(Q,)r(Pu.)-n(n +1)^/4

bi = —r. [3-2] Z[r (Q.) ] ' -n(n +1)^/4 i=l

a, = (l-bi)(n+l)/2. [3-3]

ai and bi are the two constants, which vary with different companies or

products, and n is the number of paired data of (Q, Pu).

2. Productivity-Profit model

Let P, denotes the productivity of ith lot

r(Pi): the ith rank in the ascending P series

I,: the total production cost of ith lot

Y,: The volume produced, including both quality conformed and

nonconformed products, of ith lot.

134

Then,

Pu = ( P - l ) x i - . p.4]

3. Quality-Productivity model

The model is

r(P) = a2 + b2r(Q) [3-5]

where.

n

Zr(Qi)r(P.)-n(n +1)^/4 i=l

b2 = —„ [3-6] £["•(0,)]' - n(n +1)' / 4 i = l

a2 = (l-b2)(n+l)/2. [3-7]

ai and bi are the two constants, which vary with different companies or

products, and n is the number of paired data of (Q, P).

3.2.10 Unit of Analysis

3.2.10.1 ABC Company

The units of analysis in the ABC Company were:

1. 1000 yards Gingham,

2. 1000 yards Piece-dyed fabric.

Cloth is shipped in rolls. However, because ofthe variety of customer

requirements, each roll may have different lengths. Therefore, 1000 yards was set as

the unit for measurement.

135

The unit of measurements in the ABC Company for production cost,

production quantity, revenue, profit, unit profit, quality conformance level, and

productivity were in monthly time cycles.

3.2.10.2 XYZ Company

The products of XYZ Company were made lot by lot to stock. The units of

analysis in the XYZ Company were:

1. A lot of Token Ring 16 Bit ISA IBM

This was a product of XYZ 5300 series.

2. A lot of PNP Ethernet Combo

This was a product of XYZ 1120 series.

The unit of measiu-ements in the XYZ Company for production cost,

production quantity, revenue, profit, unit profit, quality conformance level, and

productivity were in lot.

3.3 The Collection and Treatment of Data

As Leedy (1993) points out, "The data dictate the research methodology" (p.

122). Data play a crucial role in conducting research. This section specifically

describes how data was collected and treated.

136

3.3.1 Data collection

Data can be classified into two types: primary and secondary. The primary

data of this research were measured and observed directly from the companies being

studied. The secondary data of this research were obtained mainly from the treatment

ofthe primary data. The primary data of this research were collected in the field and

through the assistance of a task group in each company. Cost and revenue data were

originally collected from accoimting department. Quality data were provided by task

group. Basically, this research collected data through the use of a data collection

form (see Figure 3.10).

Production quantity was obtained by dividing the actual output quantity by its

quality conformance level. For example, if the actual output is 95 and its lot quality

is 95% conformed, then the production quantity is estimated as 100. Total

production cost included direct materials, direct labors, and overhead. This was the

cost incurred associated with the product.

3.3.2 Treatment of Data

Once data have been collected, it is necessary to consider how to deal with the

data. Each task group helped the researcher for the treatment of these data in the

following ways:

137

Page: /

COMPANY:

Date: PRODUCT:

Location:

Start Date of Production:

End Date of Production:

Inp

Lot No.

1

2

3

4

5

6

7

8

9

10

Production Quantity

ut Total Production

Cost (NTS) / (US$)

Quality records:

Equivalent Quality ofConformance (%)

Output Revenue (NTS)/ (USS)

Profit (NTS)/ (USS)

@Profit (NTS)/ OJSS)

Productivity

Figure 3.10 Data Collection Form

138

1. Data review and screening

Although data should be collected as accurately as possible, error is

inevitable. It is the responsibility ofthe researcher to pick out these errors

and mistakes according to his knowledge and expertise. Fortunately, this

research chiefly analyzed data by using the concepts of ranks, which

requires only the ordinal scale of measurement, data collected may not

need the accuracy as interval or ratio scales of measurement.

In addition, in this research, a lot of data were converted into

applicable data. For example, quality data was originally collected in

terms of defects per 1000 yards, these data needs to be converted to quality

ofConformance % for this research. Another example was the conversion

from NT$ to US$, this conversion was based on the average exchange rate

during the period of data collection.

2. Data analysis

Only the reviewed and screened data were used for statistical analysis.

Statistical software was used for data analysis. The main technique used

for this analysis was the nonparametric correlation analysis and linear

regression analysis based on ranks. The results ofthe data analysis were

examined and discussed in the following chapters to see whether the

proposed models are appropriate or not.

139

3. Data interpretation

The result ofthe data analysis were interpreted. Regardless ofthe

method used, the interpretation was made under the assumptions and

limitations of this research.

When interpreting data, consistency must be noted. For example,

when quality is proved to be positively correlated with unit profit, this

conclusion cannot be extended to state that quality is positively correlated

with profit. Besides, correlation does not necessarily imply causation, it

might be incorrect to interpret the causation based on correlation analysis.

3.4 Methodological Issues

For any valuable research, the accuracy, effectiveness, precision, bias, and

sufficiency of a research are required. Therefore, a researcher must take into account

the reliability, validity, replicability, bias, and representativeness ofthe research. In

this section, each of these five issues related to the research methodology is

addressed.

3.4.1 Reliability

"Reliability deals with accuracy" indicated by Leedy (1993, p. 42). In other

words reliable research accurately measures what the researcher intends to measure.

140

The issue of reliability in this research mainly results from two aspects: data and tools

(or instruments, machines).

Data reliability is mostly determined by the primary data. The primary data of

this research includes the production cost, revenue, and production quantity collected

by the researcher and the task force in each company. These data were collected

from the accounting systems which also provided these reliable data to management.

There are two types of problems created in the secondary data which may

result in errors in data reliability. One problem is the errors caused in observation or

recording by employees. The other problem is the measurement errors caused by the

unskillful operator. In this research, the problem of data reliability lay mainly in the

errors or mistakes made by the employee due to human error. To prevent, or

eliminate as much as possible, this type of problem of data errors or mistakes, two

solutions were provided. First, any unusual data were picked out when reviewing

collected data. Second, each employee used in the research was approved to assist in

the research due to their level of work competency.

Errors in tool reliability can be attributed to the inacciu-acy of tools,

instruments or machines. Data are the resuhs of measures from these tools (or

instruments, machines). Without correct data, the research results are useless.

Therefore, keeping the tools (or instruments, machines) accurate at all times is

crucial to collecting correct data.

141

Calibration can be regarded as "the quality control of quality control" since it

dominates the data output. The best way to prevent the error in tool reliability caused

by inaccurate tools, instruments, or machines is to make sure that these tools,

instruments, and machines are periodically calibrated to keep them operating

normally. Each company of this research had a calibration schedule, machines,

instruments, or tools were checked having been calibrated on schedule before

collecting data. Errors due to the inaccuracy of machines, instruments, or tools were

eliminated to the minimum extent.

3.4.2 Validity

Leedy (1993) indicates that "Validity is concerned with the soundness, the

effectiveness ofthe measuring instrumenf (p. 40). That is, the validity issue is

concerned yvath whether the measure is really measuring what it is expected to.

According to Leedy, the most common types of validity are: face, criterion, content,

construct, internal, and external validity.

Face validity basically asks two questions: "(1) Is the instnunent measiuing

what it is supposed to measure? (2) Is the sample being measured adequate to be

representative ofthe behavior or trait being measured?" (Leedy, 1993; p. 41). These

questions are similar to the representativeness issue, which is addressed in section

3.4.5. Since this research selected the most representative products (the largest sales

142

volume ofthe company), the research subject was adequately representative ofthe

trait being measured. Therefore, face validity was considered in this research.

Criterion validity employs a second measure to check the accuracy ofthe first

measure. Since accuracy is the main concern of reliability, it was addressed in

section 3.4.1. In addition, group discussion was employed to eliminate the potential

data errors. The check for the accuracy ofthe first measurement was taken into

account.

Content validity is concerned v^th whether the intended factors or situations

are measured. The research method of section 3.2.5 addressed the content validity.

The intended factors were collected and analyzed by the researcher and the task

force, which consisted of experienced engineering representatives, thus content

validity was addressed in this research.

Construct validity deals yvith whether the construct itself is actually measured.

Since this research followed a definite methodology, construct validity is taken into

account.

Internal validity is the "freedom from bias in forming conclusions in view of

the data" (Leedy, 1993; p. 41). Because this research conducted statistical analysis,

the change in the dependent variable was influenced by the independent variable

rather than the research design or the researcher. Therefore, internal validity was

addressed in this research.

143

External validity is related to the generalizability ofthe conclusions drawn

from a sample. Since hypotheses testing of this research were tested based on the

sample, the result of testing undoubtedly possesses external validity because ofthe

trait of statistics. However, the mathematical model developed is limited when

generalized to other cases.

3.4.3 Replicability

Replicability is concerned with the precision of measiu-ement. In theory,

given the same circumstances, research conducted by different researchers on a

specific problem should yield the same results. Replicability is the extent ofthe

consistency; therefore, it is also called repeatability.

Replicability, in essence, does not guarantee that research can achieve what

the researcher intends and expects to determine; however, good research must be

replicable so that other researchers may get identical results. Because this research

specified the research environment, variables, parameters, and definitions, and

followed the research design and methodology, the replicability issue has been taken

into account. Any deviations from the research design has been noted and reported.

^ In statistical terms, mean relates to the accuracy while standard deviation relates to the precision. An accurate mean may not be precise, and vice versa.

144

3.4.4 Bias

Leedy (1993) emphasized that bias is inevitably inherent in all research, and is

usually not perceptible especially in descriptive survey research. Bias often enters the

research design in several ways. First, bias is created through sampling methods

which do not result in representative samples. That is, not all ofthe possible samples

are considered, histead, some portion ofthe population is neglected. For instance,

when sampling from the telephone directory to conduct a survey on the general

consumer's opinion, those consumers who are not listed in the directory are

neglected.

Second, inappropriate interpretation or inference can produce bias. A

researcher may exaggerate an explanation or inference based on the facts available.

For example, based on the results found in a small-sized sample, the researcher may

apply his/her findings to a large population. This creates a problem in the confidence

level in the research.

Third, the researcher's personality can also generate bias. That is, the

subjectivity, preference, intention, and other personality traits may affect data

collection, analysis, research method, and conclusions in the research. For example,

when interviewing subjects, a researcher may spend more time talking to a subject

with whom he/she feels more comfortable, and less time interviewing a subject

whom he/she does not like to talk to. This could possibly distort the facts and hence,

cause the problem of bias.

145

In addition, bias is caused by the order the questions asked. That is, when

asking questions, the order ofthe questions is likely to affect the answers. This

problem is especially significant in interviev^ng and questionnaires. If questions are

not interesting, or are too long, the respondent may lose interest and fail to answer all

questions completely and honestly. Therefore, the answers to latter questions may

not reflect the truth.

Finally, bias may be generated through the wording. That is, some

controversial, arguable, paradoxical, or imdefined words may result in incorrect

answers. For example, if the product quality is not clearly defined, the question, "Do

you think the product quality is good or not?" is very likely to create bias among

different respondents.

Since this research is not descriptive, the problem of bias is not as prevalent

as in qualitative research. However, as Leedy stressed, bias always exists. The

researcher attempted to eliminate the bias as much as possible. This research

followed the statistical principals to avoid the sampling and confidence biases. In

addition, this research employed a task group to assist in data collection, definition,

and measurement to ameliorate any bias by the researcher in establishing these

measures. Finally, the group work reduced the individual personality bias as well as

wording bias.

146

3.4.5 Representativeness

Representativeness deals with the generalizability of research. It may not be

possible to generalize the conclusion of a research project to the similar problems of

other research which is conducted under different circumstances. Each research

project must indicate the extent to which the research may be generalized. In general,

the conclusion of theoretical research is more generalizable than that of a case study

because each case study is, by its nature, bounded by special circumstance. However,

it is not implied that research yvith higher generalizability is more valuable than the

research with lower generalizability.

In this research, the proposed mathematical models and the hypotheses which

state the positive relationships between quality and profit, productivity and profit, and

quality and productivity, can be generalized to manufacturing companies. In

addition, the approach to establish and test the specific models is also generalizable.

The fact that the specific models might not be generalizablly applied to other cases is

acknowledged. However, a specific model can be set up for a specific case by

following the procedures presented in this research.

3.5 Research Constraints

While the limitations described in section 1.3.1 are from a broader viewpoint,

this research still has additional limitations which have not been specifically

mentioned. In fact, it is difficult to list all ofthe limitations since any specific

147

condition of research is a potential limitation. However, several important

limitations of this research in addition to the limitations of sec 1.3.1 must be

addressed.

I Only two products are studied in each case company. Although each

company had many types of products, it was difficult, based on time and

cost constraints, to investigate all of their products.

2. Because the products ofthe XYZ Company were made to stock, its revenue

was estimated by the product of expected selling price and production

quantity. It was likely that a few factors, such as discounts, may affect

revenue.

3. To avoid the influence on the data analysis, all measiu-es in terms of dollars

were applied a fixed exchange rate between the NT$ and US$.

4. Although the same terms were used, e.g., product nonconformance, the

definitions may be different among the companies. Therefore, it is possible

to have a term based on different definitions in different companies.

5. Low product quality levels may invalidate result in the proposed models.

The proposed mathematical models were developed based on the important

assumption that "all quality conformed products can be sold." That is, only

when quality conformance levels meet customer requirements, can all

products be accepted and the manufacturer gains profit from the customer.

148

CHAPTER 4

FIELD STUDY RESULTS, ANALYSIS, AND DISCUSSION

This chapter presents the data collected, analysis ofthe results, and general

discussion. All data presented here were collected in a field study conducted from

June through October of 1996 m Taiwan. Data of ABC Company were collected in

months while data of XYZ Company were in lots. Before starting data collection,

definitions of quality and productivity for separate participating companies were first

determined. Both primary and secondary data are addressed in this chapter. The

primary data include production cost, revenue, and production quantity. The

secondary data consists of profit and productivity, and product quality. These data

were collected, screened, and converted to the desired form of this research.

Figure 4.1 depicts the sequence of this chapter. The task force in each

company assisted the researcher in dealing with the data collection, including primary

and secondary data. This is introduced in section 4.1. Results of data collection are

presented in section 4.2. Based on the results of collected data, hypotheses were

tested to verity the relationships of Quality-Profit, Productivity-Profit, and Quality-

Productivity. This is presented in section 4.3. Model analysis regarding the three

relationships in each company are also presented in section 4.3. Finally, a general

discussion of these relationships are addressed in the last section, section 4.4.

149

•>v

Researcher and task force

o C/3

Primary data Secondary data

Definitions •Quality •Productivity

r ^ Production

cost Revenue

Z/1

Productivity

I Confirmatory analysis •Quality-Profit •Productivity-Profit •Quality-Productivity

^ Model analysis

•Quality-Profit •Productivity-Profit •Quality-Productivity

cn

c

O

General discussion

C/3

Figure 4.1 Research Sequence of Chapter 4

150

4.1 Introduction

This section introduces company contacts and presents the data collected in

the field study. Subsection 4.1.1 briefly introduces the company contacts in the two

companies used in the research endeavor. Definitions of quality and productivity are

presented in section 4.1.2. Primary data and secondary data are addressed in

subsections 4.1.3 and 4.1.4, respectively.

4.1.1 Company Contacts

In each ofthe two companies of this study, an informal task force was

organized to help the researcher conduct this study. Due to the fact that most data

used in this research are confidential and members ofthe task force are more familiar

with the production, this research needed their assistance. The study was conducted

under the permission ofthe president in each company. All members ofthe task

forces were chosen partially due to their interests in the topic of this research.

Definitions of quality and productivity were discussed together y^th members of task

force. Secondary data were also collected through their aids. In the ABC Company,

an experienced plant manager and two colleagues, his assistant and the QC manager,

ardently supported this research. In the XYZ Company, this research was assisted by

the director of operations and two division managers, manager of manufacturing and

chief of QA.

151

Both companies emphasized that part ofthe data, especially the production

cost and revenue, could be valuable information to their competitors. The researcher

was required not to reveal their company names.

4.1.2 Operation Definition

Operafion definition of this research includes the definitions of quality and

productivity in the two companies (Table 4.1). These definitions were acquired from

group discussion and are used for the selected products of these two companies. The

definitions may not be applicable to other similar products or companies because they

are customer-oriented; and customer needs vary in different products and companies.

Definition of product quality in the ABC Company is completely determined

by the customer orders. For this research, product quality is measured by quality

conformance level (%). In the XYZ Company, products with defects are not allowed

to sell. In other words, the finished products quality must be 100% conformance.

For management purposes, quality must be measured and controlled during the

process. Quality conformance level (%) is used for measuring the product quality

within process.

The definitions ofproductivity in both companies are nearly the same.

However, the total revenue of XYZ company is based on the expected revenue, not

the actual revenue. Actual revenue is difficult to realize imless the products are sold

out, because all products in the XYZ Company are made to stock, actual revenue is

152

II

not a feasible measure. On the other hand, in the ABC Company, total revenue is

easier to realize because their products are made to specific customers. Therefore,

total revenue is the actual revenue in the ABC Company.

Table 4.1 Definitions of Quality and Productivity in the ABC and XYZ Companies

ABC Company

XYZ Company

Definition of Quality

Quality is the extent to which customer specifications are met. The specifications are usually in terms of number of defects per one thousand yards. For this research, quality conformance level is operationally defined as a ratio of the number of conformed yards to the total yards produced.

Quality is the determined by customer's satisfaction. Specifically, for management purposes, quality conformance level is operationally defined as a ratio of the number of conformed goods to the scheduled production quantity in the manufacturing process.

Definition of Productivity

Productivity is the Total Productivity. This is a ratio ofthe total actual revenue of products sold to the total production cost incurred in a profit center within a specified period.* This period is usually measured in one month intervals.

Productivity is the Total Productivity. This is a ratio of the total expected revenue of products sold to the total production cost inciuTcd for a lot in the company. Total expected revenue of a product is defined as the selling price times the number of finished goods.

* Definition ofproductivity used in this research was presented in section 2 4.1.2. The measurable input of a product is regarded as equivalent to the total production cost associated with the product in the field study.

153

4.1.3 Primary Data Collected

Three major primary data required for this study were collected in each

company. These data were production cost, revenue, and production quantity. Other

minor data, lot number, were also recorded. Lot number indicates the sequence of

production lots in the XYZ Company. According to the lot sequence, data were

tested for independence of time.

Production cost and revenue data were specially essential to this research.

The analysis of this research concentrated on the profit-based relationships.

According to the definition of this research, profit is the difference between revenue

and production cost. That is, profit data were determined from these two types of

data. These production cost and revenue data were collected by the assistance from

the accoimting department in each company.

In addition to the production cost and total revenue, production quantity was

also important to this research. Because this research relates quality and productivity

based on unit profit, which is an average profit, production quantity were collected

for calculating the unit profit. In each company, the calculation of unit profit

assumed each product in the same lot or month has equal contribution to the profit.

4.1.4 Secondary Data Collected

Three secondary data were collected. Profit data were easily secured by

subtracting production cost from total revenue. Original quality data were collected

154

and transformed into desired conformance level(%). The inspection points that

identify defects in the products of each company are listed in Appendix B. In both

companies, quality was not expressed in conformance level (in ABC, it is the number

of defects per 1000 yards while in XYZ, the finished product must be 100%

conformed). For the purpose of comparing variables in this research, all quality data

were converted to conformance level (%). These quality data were attained by

converting the available quality records into the desired % (see the definitions of

quality for each company in the previous subsection 4.1.2).

Productivity data were acquired through the calculation of revenue to

production cost. In both companies, productivity was defined as the ratio of revenue

to production cost. Like profit, productivity data were also easily calculated when

both production cost and revenue data were available.

The monetary unit used in the remaining sections is US dollars. Since the two

companies are in Taiwan, the original costs, revenue, and profit are all in New

Taiwan Dollars (NT$). During the studying period, the average exchange rate

between US$ and NT$ was close to 1: 27.5. ' For this research, all monetary data

collected in NT$ were converted into USS according to this average exchange rate.

• According to the China Times of Taiwan, the exchange rate between USS and NTS fluctuated approximately between 27.3 to 27.7 during the studying period fi-om June to October of 1996. Therefore, the average exchange rate 27.5 was used.

155

All the results of collected data are presented in the next section. Based on

these data, a statistical analysis and general discussion are conducted in the following

sections 4.3 and 4.4.

4.2 Results of Collected Data

This section presents the results of data collected in the field study. Sections

4.2.1 through 4.2.5 present these data which are summarized based on separate

products in each company. The data collected in the ABC Company were measured

in months while in the XYZ Company, they were measured in lots. This was because

the production process in ABC Company was flow-type, it adopted a process costing

system. On the other hand, the XYZ Company made products to stock and produces

lot by lot, so the batch costing system was used.

4.2.1 Production Cost Data

Tables 4.2 and 4.3 show the production cost data collected in the three

factories. A, B, and C of ABC Company for gingham and piece-dyed fabric

respectively. The number, in thousands of yards, in the last column, stands for the

production quantity of each month. Tables 4.4 and 4.5 list the production cost data

collected in the XYZ Company.

156

Table 4.2 Production Cost Data of Gingham in the ABC Company (in US$)

June

July

August

September

October

Factory A

544,510.65

457,143.26

470,970.24

440,832.05

461,832.16

Factory B

228,982.11

192,767.36

221,059.74

202,483.25

192,685.63

Factory C

152,190.46

103,122.88

122,656.30

100,389.97

130,191.95

Remarks

4337k yards

4024k yards

4216k yards

3316k yards

3790k yards

Table 4.3 Production Cost Data of Piece-dyed Fabric in the ABC Company (in USS)

June

July

August

September

October

Factory A

70,250.79

93,349.68

89,570.30

111,335.61

77,768.43

Factory B

29,542.44

39,363.52

42,041.70

57,025.54

32,446.55

Factory C

19,635.06

21,057.92

23,327.08

28,272.92

21,923.17

Remarks

957k yards

1054k yards

103 Ik yards

1089k yards

877k yards

Table 4.4 Production Cost Data of Token Ring in the XYZ Company (in USS)

Lot#

6147T

6152F

6158T

6164T

6169F

61741

6188F

6217T

6236F

6254T

Cost

33776.1

31681.2

27060.3

64326.7

36828.6

40734.1

31292.9

22965.5

34817.8

31010.9

Lot#

6256T

6257F

626 IT

6268F

6276T

6302F

6308T

631IT

6315T

6316F

Cost

36792.4

32345.4

28392.3

32283.5

38844

29052.4

29246

35712.6

34048.9

36345.7

Lot#

6322T

6327F

6335F

634 IF

6352T

6355T

6362F

Cost

28152.1

34986.5

38471.8

36928

30492.2

37008.7

29692.5

157

Table 4.5 Production Cost Data of PNP Ethernet Combo in the XYZ Company (in USS)

Lot#

5115F

5124T

5125T

5166F

5169T

5187F

520 IF

5207T

5213F

5216F

Cost

9660.7

10881.2

9827 4

10410.9

10803.2

9976.6

9744.2

9984.3

9405.3

9366.5

Lot#

5217T

5223F

5244F

5257T

5287F

5312F

5346T

5366F

5371F

5378F

Cost

10465.6

10439.1

9305.4

9483.8

9390.4

8391.6

8110.1

9678.5

8816.1

8764.9

Lot#

5379T

5394F

5432T

5435T

5445F

5458T

5465F

5467T

5488T

Cost

8978.4

9715.4

9804.8

9900.8

9541.7

9576.7

10016.5

9436.4

8372.6

4.2.2 Revenue Data

Tables 4.6 and 4.7 list the revenue ofthe two products in each factory in the

ABC Company. Tables 4.8 and 4.9 are the revenue data ofthe two products in the

XYZ Company.

Table 4.6 Revenue Data of Gingham in the ABC Company (in USS)

June

Juh

August

September

October

Factory A

621,276.01

521,882.45

531,607.87

509,780.66

520,304.92

Factory B

260,228.47

219,067.21

254,049.29

220,168.45

226,664.20

Factory C

127,612.37

79,931.91

95,556.74

82,056.93

112,448.87

Remarks

4337k yards

4024k yards

4216k yards

3316k yards

3790k yards

158

Table 4.7 Revenue Data of Piece-dyed Fabric in the ABC Company (in USS)

June

July

August

September

October

Factory A

80,864.61

106,569.56

101,102.52

128,569.98

87,614.72

Factory B

36,154.06

44,734.01

48,315.73

62,006.23

39,568.23

Factory C

16,844.41

17,622.28

18,573.22

23,109.76

19,935.39

Remarks

957k yards

1054k yards

103 Ik yards

1089k yards

877k yards

Table 4.8 Revenue Data of Token Ring in the XYZ Company (in USS)

Lot#

6147T

6152F

6158T

6164T

6169F

6174T

6188F

6217T

6236F

6254T

Revenue

48192

42455

35288

44176

51006

50130

44115

30052

45632

39564

Lot#

6256T

6257F

626 IT

6268F

6276T

6302F

6308T

631 IT

6315T

6316F

Revenue

56016

44445

34380

36348

51444

35940

41384

44459

45328

42750

Lot#

6322T

6327F

6335F

634 IF

6352T

6355T

6362F

Revenue

35724

52785

49028

45408

40838

51390

37661

Table 4.9 Revenue Data of PNP Ethernet Combo in the XYZ Company (in USS)

Lot#

5115F

5124T

5125T

5166F

5169T

5187F

5201F

5207T

5213F

5216F

Revenue

13238

14043

14911

14472

15507

13090

13824

14368

13429

13266

Lot#

5217T

5223F

5244F

5257T

5287F

5312F

5346T

5366F

5371F

5378F

Revenue

14743

15082

14328

13896

13775

12841

11655

16003

14355

13456

Lot#

5379T

5394F

5432T

5435T

5445F

5458T

5465F

5467T

5488T

Revenue

13717

14737

13716

15494

14297

15674

15197

14681

12422

159

4.2.3 Profit Data

Tables 4.10 and 4.11 list the profit ofthe two products in each factory in the

ABC Company. Profit divided by the production quantity yields the unit profit per

1000 yards. The numbers in the parentheses are unit profit per 1000 yards. Ranked

data of unit profit are also shown because they were used in the next sections.

Table 4.10 Profit Data of Gingham in the ABC Company (in USS)

June

July

August

September

October

Factory A

76765.36

(17.70) Rank: 4

64,739.19

(16.09) Rank: 3

60,637.63

(14.38) Rank: 1

68,948.61

(20.79) Rank: 5

58,472.76

(15.43) Rank: 2

Factory B

31,246.36

(7.20) Rank: 3

26299.85

(6.54) Rank: 2

32,989.55

(7.82) Rank: 4

17,685.20

(5.33) Rank: 1

33,978.57

(8.97) Rank: 5

Factory C

-24,578.09

(-5.67) Rank: 3

-23,190.97

(-5.76) Rank: 2

-27,099.56

(-6.43) Rank: 1

-18,333.04

(-5.53) Rank: 4

-17,743.08

(-4.68) Rank: 5

Remarks

4337k yards

4024k yards

4216k yards

3316k yards

3790k yards

Table 4.11 Profit Data of Piece-dyed Fabric in the ABC Company (in USS)

June

July

August

September

October

Factory A

10,613.82

(11.09) Rank: 1

13,219.88

(12.54) Rank: 4

11,532.22

(11.19)) Rank: 2

17,234.37

(15.83) Rank: 5

9,846.29

(11.23) Rank: 3

Factory B

6,611.62

(6.91)

5,370.49

(5.10)

6,274.03

(6.09)

4,980.69

(4.57)

7,121.68

(8.12)

Rank: 4

Rank: 2

Rank: 3

Rank: 1

Rank: 5

Factory C

-2,790.65

(-2.92)

-3,435.64

(-3.26)

-4,753.86

(-4.61)

-5,163.16

(-4.74)

-1,987.78

(-2.27)

Rank: 4

Rank: 3

Rank: 2

Rank: 1

Rank: 5

Remarks

957k yards

1054k yards

103 Ik yards

1089k yards

877k yards

160

Tables 4.12 and 4.13 list the profit data ofthe two products in the XYZ

Company. Data of unit profit and ranks of unit profit are also included.

Table 4.12 Profit Data of Token Ring in the XYZ Company (in USS)

Lot#

6147T

6152F

6158T

6164T

6169F

6174T

6188F

6217T

6236F

6254T

Profit

14415.9

(9.01) Rank: 25

10773.8

(7.18) Rank: 18

8227.7

(6.86) Rank: 14

9849.3

(6.16) Rank: 10

14177.4

(7.88) Rank: 20

9395.9

(5.22) Rank: 4

12822.1

(8.55) Rank: 23

7086.5

(7.09) Rank: 17

10814.2

(6.76) Rank: 13

8553.1

(6.11) Rank: 8

Lot#

6256T

6257F

626 IT

6268F

6276T

6302F

6308T

631 IT

6315T

6316F

Profit

19223.6

(10.68) Rank: 27

12099.6

(8.07) Rank: 22

5987.7

(4.99) Rank: 3

4064.5

(3.39) Rank: 1

12600

(7.00) Rank: 15

6887.6

(5.74) Rank: 7

12138

(8.67) Rank: 24

8746.4

(5.47) Rank: 6

11279.1

(7.05) Rank: 16

6404.3

(4.27) Rank: 2

Lot#

6322T

6327F

6335F

634 IF

6352T

6355T

6362F

Profit

7571.9

(6.31) Rank: 12

17798.5

(10.47) Rank: 26

10556.2

(6.21) Rank: 11

8480

(5.30) Rank: 5

10345.2

(7.39) Rank: 19

14381.3

(7.99) Rank: 21

7968.5

(6.13) Rank: 9

161

Table 4.13 Profit Data of PNP Ethernet Combo in the XYZ Company (in USS)

Lot#

5115F

5124T

5125T

5166F

5169T

5187F

5201F

5207T

5213F

5216F

Profit

3577.3

(6.39) Rank: 5

3161.8

(5.10) Rank: 1

5083.6

(8.20) Rank: 24

4061.1

(6.77) Rank: 8

4703.8

(7.35) Rank: 16

3113.4

(5.37) Rank: 2

4079.8

(6.80) Rank: 4

4383.7

(6.85) Rank: 25

4023.7

(7.06) Rank: 11

3899.5

(7.09) Rank: 6

Lot#

5217T

5223F

5244F

5257T

5287F

5312F

5346T

5366F

5371F

5378F

Profit

4277.4

(6.90) Rank: 14

4642.9.

(7.37) Rank: 10

5022.6

(8.371) Rank: 19

4412.2

(7.61) Rank: 9

4384.8

(7.31) Rank: 15

4449.4

(8.24) Rank: 20

3544.9

(7.09) Rank: 3

6324.5

(9.73) Rank: 28

5538.9

(9.55) Rank: 27

4691.1

(8.38) Rank: 13

Lot#

5379T

5394F

5432T

5435T

5445F

5458T

5465F

5467T

5488T

Profit

4738.6

(8.17) Rank: 22

5021.6

(8.10) Rank: 23

3911.2

(6.52) Rank: 7

5593.2

(8.74) Rank: 26

4755.3

(8.20) Rank: 12

6097.3

(9.68) Rank: 29

5180.5

(7.97) Rank: 21

5244.6

(8.46) Rank: 18

4049.4

(7.79) Rank: 17

4.2.4 Quality Data

Tables 4.14 and 4.15 list the quality conformance level data in the ABC

Company, while Tables 4.16 and 4.17 represent the data of XYZ Company. Ranked

data of quality are also shown in the parentheses.

162

Table 4.14 Quality Conformance Level of Gingham in

June

July

August

September

October

Factory A

97.80% (4)

97.28% (3)

96.33% (1)

97.83% (5)

96.50% (2)

Factory B

97.86% (3)

97.65% (2)

98.16% (4)

97.50% (1)

98.64% (5)

Facton, C

96.83% (3)

96.80% (2)

96.35% (1)

97.62% (4)

98.74% (5)

The values in parentheses ( ) located in each cell indicate the respective rank ofthe field data in that cell.

Table 4.15 Quality Conformance Level of Piece-dyed Fabric in the ABC Company (in USS)*

June

JuK

August

September

October

Factory A

97.91% (4)

97.86% (3)

97.51% (1)

98.73% (5)

97.55% (2)

Factory B

98.32% (3)

98.1% (2)

98.53% (4)

97.50% (1)

98.64% (5)

Factors C

97.78% (4)

97.18% (3)

96.53% (2)

96.09% (1)

98.08% (5)

* The values in parentheses ( ) located in each cell indicate the respective rank ofthe field data in that cell.

Table 4.16 Quality Conformance Level of Token Ring in the XYZ Company (in USS) Lot#

6147T

6152F

6158T

6164T

6169F

6174T

6188F

6217T

6236F

6254T

Quality

96.88% (25)

95.67% (18)

93.83% (9)

93.94% (12.5)

96.00% (21)

92.72% (4)

96.53% (23)

95.20% (17)

94.06% (14)

93.64% (8)

Lot#

6256T

6257F

626 IT

6268F

6276T

6302F

6308T

6311T

6315T

6316F

Quality

96.94% (26)

96.13% (22)

92.33% (2.5)

92.08% (1)

94.16% (15)

93.08% (7)

96.79% (24)

92.94% (6)

94.56% (16)

92.33% (2.5)

Lot#

6322T

6327F

6335F

634 IF

6352T

6355T

6362F

Quality

93.92% (11)

97.06% (27)

93.94% (12.5)

92.81% (5)

95.79% (19)

95.94% (20)

93.85% (10)


163

Table 4.17 Quality Conformance Level of PNP Ethernet Combo in the XYZ Company (in USS)*

Lot#

5115F

5124T

5125T

5166F

5169T

5187F

520 IF

5207T

5213F

5216F

Quality

91.43% (3)

90.32% (1)

95.48% (26)

92.50% (5)

94.38% (13)

91.03% (2)

93.17% (7)

93.44% (8)

92.98% (6)

93.64% (9)

Lot#

5217T

5223F

5244F

5257T

5287F

5312F

5346T

5366F

5371F

5378F

Quality

93.87% (10)

94.440/0 (14)

95.50% (27)

94.48% (15)

94.17% (11)

95.19% (22)

94.20% (12)

95.38% (25)

95.69% (28)

95.18% (21)

Lot#

5379T

5394F

5432T

5435T

5445F

5458T

5465F

5467T

5488T

Quality

94.83% (18)

94.84% (19)

91.50% (4)

95.31% (23)

95.17% (20)

95.87% (29)

94.77% (17)

95.32% (24)

94.62% (16)

* The values cell.

in parentheses ( ) located in each cell indicate the respective rank ofthe field data in that

4.2.5 Productivity Data

Tables 4.18 through 4.21 are the productivity data ofthe two companies.

Niunbers in the parentheses are the ranks ofproductivity.

Table 4.18 Productivity Data of Gingham in the ABC Company (in USS)"

June

July

August

September

October

Factory A

114.10% (3)

114.16% (4)

112.88% (2)

115.64% (5)

112.66% (1)

Factory B

113.65% (3)

113.64% (2)

114.92% (4)

108.73% (1)

117.63% (5)

Factory C

83.85% (4)

77.51% (1)

77.91% (2)

81.74% (3)

86.37% (5)


164

Table 4.19 Productivity Data of Piece-dyed Fabric in tv»p. ARr r-r tvi o T, ,« T TQC\*

June

July

August

September

October

Factory A

115.11% (4)

114.16% (3)

112.88% (2)

115.48% (5)

112.66% (1)

Factory B

122.38% (5)

113.64% (2)

114.92% (3)

108.73% (1)

121.95% (4)

Factory C

85.79% (4)

83.68% (3)

79.62% (1)

81.74% (2)

90.93% (5)


Table 4.20 Productivity Data of Token Ring in the XYZ Company (in USS)* Lot#

6147T

6152F

6158T

6164T

6169F

6174T

6188F

6217T

6236F

6254T

Productivity

142.68% (25)

134.01% (19)

130.41% (13)

128.69% (12)

138.50% (21)

123.07% (5)

140.97% (23)

130.86% (14)

131.06% (15)

127.58% (11)

Lot#

6256T

6257F

626 IT

6268F

6276T

6302F

6308T

6311T

6315T

6316F

Productivity

152.25% (27)

137.41% (20)

121.09% (3)

112.59% (1)

132.44% (16)

123.71% (6)

141.50% (24)

124.49% (7)

133.13% (17)

117.62% (2)

Lot#

6322T

6327F

6335F

6341F

6352T

6355T

6362F

Productivity

126.90% (9)

150.87% (26)

127.44% (10)

122.96% (4)

133.93% (18)

138.86% (22)

126.84% (8)


Table 4.21 Productivity Data of PNP Ethernet Combo in the XYZ Company (in USS)* Lot#

5115F

5124T

5125T

5166F

5169T

5187F

520 IF

5207T

5213F

5216F

Productivity

137.03% (3)

129.06% (1)

151.73% (20)

139.01% (4)

143.54% (10)

131.21% (2)

141.87% (8)

143.91% (12)

142.78% (9)

141.63% (7)

Lot#

52I7T

5223F

5244F

5257T

5287F

5312F

5346T

5366F

5371F

5378T

Productivity

140.87% (6)

144.48% (13)

153.98% (24)

146.52% (14)

146.69% (15)

153.02% (22)

143.71% (11)

165.35% (29)

162.83% (27)

153.52% (23)

Lot#

5379T

5394F

5432T

5435T

5445F

5458T

5465F

5467T

5488T

Productivity

152.78% (21)

151.69% (18)

139.90% (5)

156.50% (26)

149.84% (17)

163.67% (28)

151.72% (19)

155.58% (25)

148.36% (16)


165

4.3 Data Analysis

Data analysis in this section is divided into two parts: confirmatory analysis

and model analysis. The former is to test the collected data to confirm the alternative

hypotheses proposed in Chapter 3. The latter identifies the models and assesses the

aptness of models for the studied companies. Statistical approaches, especially the

nonparametric correlation analysis and regression analysis, are used throughout this

section. Results of analysis are all summarized with tables.

4.3.1 Confirmatory Analysis

This section deals with the hypotheses tests mentioned in Figures 3.1 and 3.2

of section 3.2.3. The purpose of these tests is to confirm the positive Quality-Profit,

Productivity-Profit, and Quality-Productivity relationships in the studied

manufacturing environments. Since profit is highly dependent on the sales quantity,

unit profit is more meaningful to be used to compare with quality conformance level

and productivity.

The method of this confirmatory analysis is first introduced in subsection

4.3.1.1. According to this method, hypotheses are tested in the order of Quality-

Profit, Productivity-Profit, and Quality-Productivity relationships in subsections

4.3.1.2, 4.3.1.3, and 4.3.1.4, respectively.

166

4.3.1.1 Method of Analysis

The hypotheses presented in Figures 3.1 and 3.2 were tested by correlation

analysis. Because quality conformance level has different meanings to different

products, factories, and companies, rank correlation analysis was used. There are a

couple of methods developed for the computation of rank correlation, the most

commonly used measure. Spearman's Rho, was used to calculate the rank correlation

coefficient.

Based on the rank correlation coefficients calculated for various products,

factories, and companies, hypotheses were tested and conclusions were drawn.

Because the purpose of this subsection, section 4.3.1, is to test the positive correlation

of Quality-Profit, Productivity-Profit, and Quality-Productivity relationships, one-

tailed test was adopted.

After obtaining conclusions from hypotheses tests for all products, factories,

and companies, the confidence intervals ofthe correlation coefficients were

estimated to see the degree these variables correlate with each other. These intervals

reveal the smallest correlation coefficients in each relationships.

Since rank correlation analysis is a distribution-fi-ee approach, it is not

necessary to assume a distribution the population is subject to. However, when using

Spearman's Rho method for analysis, there are basic assumptions:

1. Data samples are random samples.

2. Data must be paired data.

167

3. Each data can be assigned a value according to its rank. In the case of ties,

the value ofthe average ofthe ranks would be assigned to each ofthe ties.

The analytical steps for subsection 4.3.1 are illustrated as follows:

I. Compute Spearman's Rho

If no ties or a moderate number of ties,

6T p=\-

n(n^- l ) ' [4-1]

where

p = correlation coefficient

n = number of paired data

T=Z[r(X,)-r(Y,)r i = l

where

r(Xi) is the rank of ith sample of variable X

r(Y,) is the rank of ith sample of variable Y.

Or, if there are many ties,

^ n+1 , Zr(X.)r(Y.)-n(-—)^ 1=1 ±

^ ~ x^ , n-i-1 , , , v^ , n + 1 , , , 14-21 [ £ r ( X . ) ^ - n ( ^ - ) ^ ] ' ^ [Er(Y.)^-n(—-)^] '^ ^ ^

1=1 ^ 1=1 ^

2. Spearman's Rho test

This is an one-tailed test for positive correlation.

168

HQ: The Xj and Yj are mutually independent

H,: There is a tendency for the larger values of X and Y to be paired

together

Crifical region, Wp, is determined from the quantiles of p listed in the

Appendix C. If computed p is greater than or equal to the critical

region, HQ is rejected.

3. Test the normality of observed data by using the Lilliefors normality test.

4. Estimate confidence intervals of correlation coefficients.

4.3.1.2 Quality-Profit Analysis

4.3.1.2.1 Spearman's Rho Test

Table 4.22 summarizes the hypotheses tests results by using the Spearman's

Rho test method. Hypotheses of Quality-Profit relationship are identical for the

different products and factories of this research. The value of Wp is the critical

region and is obtained from Table C. 1 in Appendix C. The Spearman's Rho, p, was

calculated by [4-1] since there were no ties (in all cases ofthe ABC Company and the

PNP case of XYZ Company) or a small nimiber of ties (two ties exists in the quality

conformance level of Token ring case ofthe XYZ Company) in the data. If p is

greater than or equal to Wp, then accept Hi; otherwise, accept HQ. ^

^' Although other statisticians would rather to state "reject Ho " than to state "accept Hi", Dr Conover thinks it is the same. Since the nonparametric statistical approaches used in this research are mainly according to his book (1980), this research adopts his viewpoints. Also, "accept HQ" is equal to "failed to reject HQ."

169

Table 4.22 Summary of Spearman's Rho Test Resuhs for Quality-Profit Relationship

Ho: The quality conformance level and unit profit are muUially independent

HI ! There is a tendency for the larger values of quality conformance level and unit profit to

be paired together

Significance level: a = 0.05

Company

ABC

XYZ

Product

Gingham

Piece-dyed fabric

PNP

Token Ring

Factory A

Critical region: Wp = 0.800

Computed Rho: p=1.00

Conclusion: Accept Hi


Computed Rho: p = 0.400

Conclusion: Accept HO

Factory B







Factory C







Critical region: Wp = 0.3113 Computed Rho: p = 0.9744 Conclusion: Accept Hi


Except piece-dyed fabric in Factory A, all alternative hypotheses are

accepted. That is, except piece-dyed fabric in Factory A (see Table 4.22), quality

conformance level shows positive correlation with unit profit at a 95% confidence

level. The decision of accepting the null hypothesis in the case of piece-dyed fabric

170

in Factory A does not mean that HQ is true. It just indicates that Ho has not been

proven to be false. That is, although the conclusion in the case of piece-dyed fabric

in Factory A is to accept HQ, it does not mean that its quality conformance level does

not correlate with unit profit.

4.3.1.2.2 Normality Test

The results ofthe Lilliefors normality test for the sample data of quality and

imit profit are shown in the Appendix D, Figures D. 1 through D.8. All figures show

that, at a 95% confidence level, the observed data subject to normality. Based on the

results, the confidence interval of correlation coefficient of Quality-Profit

relationship can be estimated.

4.3.1.2.3 Estimation of Confidence Interval of Correlation Coefficient

Since the paired data of (Q, Pu) in all cases are shown to be normally

distributed, an estimated confidence interval ofthe eight Spearman's Rhos (shown in

Table 4.22) can be obtained. Due to the fact that the standard deviation ofthe

population is unknown and sample size is small, the following formula (based on

Montgomery, 1991) is used to estimate the confidence interval of correlation

coefficient ofthe population:

p - , „ „ ^ < ^ < p + . . . ^ [4-3]

171

Substitute sample mean p = 0.9077, sample standard deviation G =^2^1^. n

" 8, to 025,7 = 2.365 into [4-3], the 95% confidence interval for the population p is

0.7339 < p < 1.0815. [4-4]

Since p cannot be greater than one, [4-4] can be rewritten as

0.7339<p<1.0. [4-5]

That means, at a 95% confidence level, the correlation coefficient of Quality-Profit

relationship based on ranks is at least 0.7339, a highly-correlated number sufficient

to verify the positive Quality-Profit relationship. Note the right-hand side of [4-4] is

reduced to one, it indicates that the confidence level could be lowered. Section 4.4

will discuss this.

4.3.1.3 Productivity-Profit Analysis


Table 4.23 summarizes the hypotheses tests results for Productivity-Profit

relationship by using the Spearman's Rho test method. Like Quality-Profit

relationship, all hypotheses for Productivity-Profit relationship are identical for the

different products and factories of this research. As before, Wp is the critical region

obtained from Table C. 1 in Appendix C and p is calculated by [4-1] because there are

no ties in all cases.

According to Table 4.23, except piece-dyed fabric in Factory A, all

alternative hypotheses are accepted. That is, except piece-dyed fabric in Factory A,

172

productivity was shown having a positive correlation with unit profit at 95%

confidence level. Similariy, the piece-dyed fabric case of accepting the null

hypothesis in the Factory A does not show that productivity does not correlate with

unit profit.

Table 4.23 Summary of Spearman's Rho Test Results for Productivity-Profit Relationship

Ho : The productivity and unit profit are mutually independent

Hi: There is a tendency for the larger values ofproductivity and imit profit to be paired

together


Company

ABC

XYZ

Product

Gingham

Piece-dyed fabric

PNP

Token Ring

Factory A


Computed Rho: p =0.800




Conclusion: Accept Ho

Factory B







Factory C









173

The resuhs ofthe Lilliefors normality test regarding the sample data of

productivity and unit profit are shown in Appendix D, Figures D.9 through D. 16. All

figures show that, at a 95% confidence level, the observed data are subject to

normality. Based on the results, the confidence interval ofthe correlation coefficient

of Productivity-Profit relationship can be estimated.


Similarly, since the paired data of (P, Pu) in all cases are shown to be

normally distributed, an estimated confidence interval ofthe eight Spearman's Rhos

(shovm in Table 4.23) can be obtained. Due to the fact that the standard deviation of

the population is unknown and sample size is small, [4-3] is also used here.

A

Substitute sample mean p = 0.8328, sample standard deviation a =0.2290, n

^ 8, to 025,7 = 2.365 into [4-3], the 95% confidence interval for the population p is

0.6413 < p < 1.0243 [4-6]

or

0.6413 < p < l . O . [4-7]

That is, at a 95% confidence level, the correlation coefficient of Productivity-Profit

relationship based on ranks is at least 0.6413. This is also a satisfactory number to

state that the Productivity-Profit relationship is positive.

174

4.3.1.4 Quality-Productivity Analysis


Tables 4.24 tabulates the results of Spearman's Rho tests for Quality-

Productivity relationship for the two companies. As before, all hypotheses for

Quality-Productivity relationship are identical. Wp is still the critical region from

Table C. 1 and p is calculated by [4-1] because there are no ties (in all cases ofthe

ABC Company and the PNP case ofthe XYZ Company) or a small number of ties

(two ties exists in the quality conformance level of Token ring case ofthe XYZ

Company).

Except for piece-dyed fabric in Factory B, all the test results prove the

positive relationship between quality and productivity at a 95% confidence level. It is

noted that, although the piece-dyed fabric case in Factory A did not show that a

positive relationships existed in the Quality-Profit and Productivity-Profit

relationships in the previous tests, it demonstrates the Quality-Productivity

relationship is positively correlated.

According to this test, it reveals another important point. If the confidence

level is reduced to 90%, then the piece-dyed fabric case in Factory B also meet the

criteria of accepting Hi (from Table C. 1, Wp is decreased to 0.700). This is an

encouraging result.

175

Table 4.24 Summary of Spearman's Rho Test Results for Quality-Productivity Relationship

Ho : The quality conformance level and unit productivity are mutually independent

Hi: There is a tendency for the larger values of quality conformance level and productivity to

be paired together


Company

ABC

XYZ

Product

Gingham

Piece-dyed fabric

PNP

Token Ring

Factory A







Factory B






Conclusion: Accept Ho

Factory C







Critical region: Wp = 0.3113 Computed Rho: p = 0.9567 Conclusion: Accept Hi Critical region: Wp = 0.3236 Computed Rho: p = 0.9792 Conclusion: Accept Hi


The results ofthe Lilliefors normality test for the sample data of quality and

productivity are shown in the Appendix D, Figures D. 17 through D.24. All figures

show that, at a 95% confidence level, the observed data are subject to normality.

Based on the results, the confidence interval of correlation coefficient of Quality-

Productivity relationship can be estimated.

176

Based on the results ofthe normality test and the eight Spearman s Rho

(shown in Table 4.24), the confidence interval of correlation coefficient ofthe ranked

Quality-Productivity relationship is estimated by [4-3].

At a 95% confidence level and sample mean p = 0.8796, sample standard

A

deviation a = 0.1044, n = 8, to 025,7= 2.365 yield the following interval

0.7923 < p < 0.9668 . [4-8]

That is, at a 95% confidence level, the correlation coefficient ofthe ranked Quality-

Productivity relationship is at least 0.7923. This number also shows that there is a

highly positively correlated relationship between quality and profit.

According to the hypotheses test and confidence interval estimation,

presented in this subsection, an encouraging result indicates the belief, that the

Quality-Profit, Productivity-Profit, and Quality-Productivity relationships are

positive, is correct. Although this results cannot reveal that how much profit could be

gained by enhancing quality or productivity, it at least indicates that the higher the

quality conformance level or productivity, a larger profit margin is possible.

The more definite relationships of Quality-Profit, Productivity-Profit, and

Quality-Productivity ofthe ABC and XYZ companies are examined in the next

subsection 4.3.2. Specific models were established so that the value of a dependent

variable could be predicted based on a given independent variable.

177

4.3.2 Model Analysis

This section presents the analysis ofthe three models proposed in section

3.2.9. Although the Spearman's Rho tests have shown that the relationships of

Quality-Profit, Productivity-Profit, and Quality-Productivity are positively correlated,

the correlation coefficients could not indicate how they correlated. It is of interest to

know the functions ofthe three relationships. This section looks at the relationships

of Quality-Profit, Productivity-Profit, and Quality-Productivity more precisely. This

section also discusses the aptness ofthe three models. It is obvious that these models

are only applied to the products, factories, and companies being studied.

4.3.2.1 Method of Analysis

Linear regression method based on ranks is used to examine the relationships

of Quality-Profit, Productivity-Profit, and Quality-Productivity. Since the correlation

ofthe relationships, Quality-Profit and Quality-Productivity, were calculated based

on ranks in the previous section and the number of observations in each case are not

large, linear regression based on ranks is applied. As to the Productivity-Profit

relationship, unit profit is directly related to productivity according to the definition

ofproductivity of this research. Therefore, it is not necessary to analyze the

relationship between productivity and unit profit based on sample data.

The linear regression method based on rank is nonparametric. This method

has two basic assumptions: (1) the sample is a random sample, (2) the regression

178

relationship is linear. Data of this research came from the production process and has

been shown to be normally distributed in the preceding subsections 4.3.1.2 through

4.3.1.4, thus the first assumption is met. As to the second assumption, Conover

(1980) indicated that if the relationship between two variables are monotonic, either

increasing or decreasing, their ranks must have a linear relationship. The results of

hypotheses tests presented in subsection 4.3.1 have shown that the ranks of quality,

unit profit, and productivity go hand-in hand. That is, the second assumption is also

met. Therefore, linear regression models can be established and analyzed based on

the ranks of variables.

The procedure for sections 4.2.2.2 through 4.3.2.4 is as follows.

1. Identify the estimated linear regression model based on ranks.

This step is to estimate the linear regression function for each case.

If the estimated model is ofthe form

r( Y) = a + b r(X) [4-9]

where r(X) and r(Y) represent the ranks of variables X and Y,

respectively. Constant a is the intercept ofthe line while b is the

slope. Both a and b are unknovm and must be estimated from the data.

2. Study the residual plot, residual time plot, and residual normality plots to

check the aptness of these specific models.

The aptness of a liner regression model can be examined by four

properties: linearity of regression fimction, constant variance of error

179

terms, independence of error terms, and normality of error terms.^

Linearity and constant variance can be inspected from a residual plot.

The residual time plot diagnoses the independence of error terms. The

residual normality plot inspects the normality of error terms.

4.3.2.2 Quality-Profit Relationship Model Analysis

This subsection first presents the specific Quality-Profit relationship models

for all cases of this research. These models are then examined by residual plots to

inspect their aptness. The plots used here to check the four properties of a linear

regression model contains plots of residuals against the ranks of quality, residuals

against time, and residuals against expected values.

4.3.2.2.1 Specific Linear Regression Models.

The estimated linear regression models ofthe Quality-Profit relationship for

the cases of this research are established and summarized in Table 4.25. Note an

important fact, except for a tiny difference in the Token ring case, the slope of each

^ Error term and residual are different concepts in linear regression analysis. Error term, e, is the vertical deviation of Y from the unknown true regression line and hence is unknown. That is, 8 = Y -E{ Y}. Residual, e, is the vertical deviation from the fitted value on the estimated regression line, and it

A

is known. That is, e = Y - Y

180

regression line is exactly equal to the correlation coefficient obtained in section

4.3.1.2 27

Table 4.25 Summary ofthe Estimated Linear Regression Models for Quality-Profit Relationship

Company

ABC

XYZ

Product

Gingham

Piece-dyed fabric

PNP

Token Ring

Factory A

Model: r(Pu) = r(Q) (a=0,b=l)

Model: r(Pu)=1.8 + 0.4r(Q)

(a=1.8, b=0.4)

Factory B


Model: r(Pu) = 0.3 + 0.9r(Q)

(a=0.3, b=0.9)

Factory C


Model: r(Pr) = r(Q) (a=0,b=l)

Model: r(Pu) = 0.3842 + 0.9744r(Q) (a=0.3842, b=0.9744)

Model: r(Pu) = 0.171 + 0.9878r(Q) (a=0.171,b=0.9878)

4.3.2.2.2 Residual Plots

4.3.2.2.2.1 Plots: Residuals Against r(Q) - Check the Linearity and Constant

Variance. Figures 4.2 exhibits the residual plots ofthe residuals against the ranks of

quality r(Q) in all cases. According to Neter, Wasserman, and Kutner (1990), except

for the Figure 4-2(d), the other seven plots did not display these models are nonlinear

or having nonconstant variances 28

^ That is, in case there are no ties, the slope of a regression line and its correlation coefficient should be the same. This relationship is proved in the Appendix E. The difference between the slope and correlation coefficient in the Token ring case lies in the situation that there are two ties in the quality data. However, since the number of ties are not two many, the difference is very small.

^ If a residual plot displays apparently a curvilinear trend, its model could be nonlinear. If there is an inward or outward funnel-type plot, it indicates the error terms may be decreasing or increasing respectively, and hence has possible nonconstant variances.

181

Residual Plot: e * r(Q)

1

0.8

1 0.6 + I 0.4 " 0.2 1

6

r(Q)

Gingham (Factory A, ABC Company) (a)

Residua I Plot: e * r(Q)

j2 ra a •o 'M 0)

OC

1

0.8

0.6 +

0.4

0.2 +

0 6

r(Q)

Gingham (Factory B, ABC Company) (b)


1 « 0.8 1 g 0.6

M 0.4

Oi 0.2

r(Q)

Gingham (Factory C, ABC Company) (c)

Res

idu

als


•7

1

0

-1

-2

-"^ -

• • •

1 2 4 (

•

r(Q)

i

Piece-dyed Fabric (Factory A, ABC Company)

(d)

Figure 4.2 Residual Plots: Residuals Against Ranks of Quality

182

22 ra 3

"35 OC

0.5

-0.5

-1

r(Q)

Piece-dyed Fabric (Factory B, ABC Company)

(e) ua

ls

Res

id

F

1 1

0.8

0.6

0.4

0.2 n

(esidual Plot: e * r(Q)

0 2 4 6

r(Q)

Piece-dyed Fabric (Factory C, ABC Company)

(f)

Res

idu

als

6 1

4

2

0

- 2 '

-4

-6


• • •

1 mmmt% i^ ^

\ **l^# ^0

r(Q)

D

PNP Ethernet Combo (XYZ Company) (g)


4 +

g 2 + "O

35 0

-2 "f

-4

1 ^ * * 2<f 3D

r(Q)

Token Ring (XYZ Company) (h)

Figure 4.2 (Continued)

183

Figure 4-2(d) needs to be further inspected. The simplest way is to calculate

and test the ranks correlation between r(Q) and r(e). It is happened that the r(Pu) is

exactly identical with r(e) for all observations of this case. According to the

Spearman's Rho test result presented in the previous Table 4.22, Figure 4-2(d) is

tested having nonconstant variance.

4.3.2.2.2.2 Plots: Residuals Against Time - Check the Nonindependence of

Error Terms. A residual time plot provides an effective approach to detect whether

the error terms are correlated over time or not. If error terms correlated with the time

sequence of data, it shows the nonindependence of error terms and the dots in the

plot must have a trend. This trend may be in a straight line with a slope greater or

less than zero, or in a curvilinear form. Figures 4.3 displays the residual time plots of

the residuals against the time sequence, r(T), ordered in months in the ABC Company

and in lot number in the XYZ Company, for all cases. These residual time plots do

not show evidences to conclude that the error terms are nonindependent.

In addition to the visual inspection on the plots, other methods may be used to

check the more complicated plots. The two complicated plots. Figures 4.3(g) and (h),

the conclusion that the ranks of data are not correlated yvith time can also be verified

by using the Durbin-Watson test. This test was developed to detect serially correlated

data. Its test procedure and table are described in Appendix F. Table 4.26

summarizes the test results of using this method (in the table, Ct is the residual at time

184

t). This results show that the error terms in this two cases are both noncorrelated with

time, and hence, the ranks of data are not dependent on time.

Residual Time Plot: e * r(T)

M

n 3

Res

id

0.8

0.6

0.4

0.2

0 2 4

r(T)

6


Residual Time Plot: e *

1

0.8

§ 0.6 •o

'35 0.4 « • 0.2

n -

r(T)

0 2 4 6

r(T)


uals

R

esid


i

0.8

0.6

0.4

0.2 n

0 2 4 e

r(T)

r(T)



1 + re 0

• o •Jfl - 1 :

oc -2 I -3

•

—H

2 4

r<T)


(d)

Figure 4.3 Residual Time Plots: Residuals Against Time Sequence

185

Res

idua

ls

Residual Plot: e * r(T)

1 -•

0.5

0 (

-0.5

-1

•

1 2 t (

•

r(T)


(e)


*

uals

o

o

b>

bo

-

•a •35 0.4 4) ^ 0.2

n -

r(T)

0 2 4 6

r(T)


(f)

Residual Time Plot: e " r(T)

22 ra 3

'55 OC

6

4

2 1-0

-2^

-4

-6

• • •

20 oD

r(T)



R

4

§ 2 •a % 0 a:

-2 _A

•

^ • ^ _ • •

) * to 2dV •s 0

r(T)



186

Table 4.26 The Durbin-Watson Test Results for the Quality-Profit Relationship of PNP and Token Ring Cases

HQ: Data are independent with time

Hi: Data are nonindependent with time

Significance level a = 0.05

Cases

PNP

Token Ring

Results

Critical region (n=29): dL=1.34, du=1.48

Computed data: X(^/ " ^t-xf ^ 223.0273, S^/^= 102.668, /=2 t=\

Z(^,-^,-,)' D = - ^ —; = 2.172

Conclusion: Since D > dy, accept Ho


w n

Computed data: X(^/ " ^/-i)' = 102.064, X^/ ' = 40.75565, 1=2 /=1

D = ^^^ = 2.504

t=\

Conclusion: Since D > du, accept Ho

187

4.3.2.2.2.3 Plots: Residuals Against Expected Values - Check the Normaliy

of Error Terms. This plot is called the normal probability plot ofthe residuals. In

this plot, each residual is plotted against its expected value. If a residuals plot

displays neariy linear form, it suggests agreement with normality. Otherwise, a plot

that departs significantly from linearity reveals that the errors is not subject to a

normal distribution.

According to Neter, Wasserman, and Kutner (1990), statistical theory has

proved that, in a random sample of n, a good approximation ofthe expected value,

EXP VALUE, ofthe ith smallest observation is given by

EXPVALUE = V M S E [ Z ( ^ ~ ' )] [4-10]

where V M S E , mean square error, is the estimated standard deviation which equals

2 i-0.375 (Ee )/(n-2) and z( TT^) is the percentile ofthe standard normal distribution.

This approximation is based on the facts that if the expected values ofthe ordered

residuals is under normality, they must meet two conditions. First, the expected value

ofthe error terms should be zero and second, the standard deviation ofthe error terms

is estimated by V M S E .

Figure 4-4 exhibits the normal probability plots of residuals ofthe specific

models.^^ The ordinate represents the ascending ordered residuals and the abscissa

stands for the residuals' correspondent expected values, obtained by [4-10].

^' There are four cases in which both the residuals and MSE are zeros. They are: Gingham in the Factory A, B, C, respectively, and Piece-dyed fabric in the Factory C. It is apparent that their error

188

Normality Plot: e * EXPVALUE

2

1

ra 0 j2 "ra 3

tc -2

-3

0.5

EXPVALUE


(a)


ra 3

•a '!« OC

0.5

0

-0.5 I

-1

di ;

EXPVALUE


(b)


ft

4

« 2 ra

5 0-5 -2

-4

-6

•

1 ]f^

EXPVALUE

;

PNP Ethernet Combo (XYZ Company) (c)

No

6

4 -ra p , 3 ^

"35 0 Oi

^ . 2 (

-4 ^

nmality Plot: e * EXPVALUE

•

1 0.5 r ^ 1 1

EXPVALUE

5

Token Ring (XYZ Company) (d)

Figure 4.4 Residual Plots: Residuals Against Expected Values

terms are all exactly subjected to normality since there are only one point in the plot. Therefore, the plots of these four cases are not included in the Figure 4.4.

189

The plot m Figure 4.4(b) shows reasonably close to a straight line. The other

three plots need to be examined further. Looney and Gulledge (1985) suggested an

approach to assess the normality. Their approach is based on the concept that the

higher correlation coefficient, the more indicative of normality. According to Looney

and Gulledges' approach, normality can be assessed by the correlation coefficient and

a critical value. If the correlation coefficient is greater than the critical value, the

error terms is under normality. Because the correlation coefficients of cases of PNP

and Token Ring are very high, 0.9744 and 0.9878, respectively, according to Looney

and Gulledges' approach, these two cases should be subjected to normality. As to the

case ofthe product piece-dyed fabric in the Factory A of ABC Company, because of

its low correlation coefficient, 0.4, it can not be concluded normal.

4.3.2.3 Productivity-Profit Relationship Model Analysis

The Productivity-Profit relationship model is directly expressed by equation

[3-4], which is from [A-21] of Appendix A. Because ofthe definitions of

productivity and profit of this research, productivity is directly related with profit, or

more precisely, with unit profit. If total cost, revenue, and quantity are given,

productivity and unit profit are easily obtained and linked.

Now that the model is established totally based on the definitions, it is not

necessary to discuss the model's aptness here. If the definitions ofproductivity and

profit of this research are used, this model is applicable.

190

4.3.2.4 Quality-Productivity Relationship Model Analysis

Like the Quality-Profit relationship model, the Quality-Productivity

relationship is linked through a linear regression line based on ranks of these two

variables. The specific Quality-Productivity relationship models for all cases of this

research are presented in section 4.3.2.4.1. These models also need inspection to see

their aptness. Section 4.3.2.4.2 deals with this analysis of model aptness by checking

the residual plots. As before, if a decision is hard to make by using visual

assessment, other auxiliary statistic tools will be applied.

4.3.2.4.1 Specific Linear Regression Models

Table 4.27 presents the estimated linear regression models ofthe Quality-

Productivity relationship for all cases being investigated. Note although the case of

piece-dyed fabric in the Factory A could not be proved as having a correlation

between Quality and unit profit, it has a higher correlation coefficient (i.e., the slope

ofthe regression line b) between Quality and Productivity.

Table 4.27 Summary ofthe Estimated Linear Regression Models for Quality-Productivity Relationship

Company

ABC

XYZ

Product

Gingham

Piece-dyed fabric

PNP Token Ring

Factory A

Model: r(P) = 0.6 + 0.8r(Q)

(a=0.6, b-0.8) Model:

r(P) = 0.3 + 0.9r(Q) (a=0.3, b=0.9}

Factory B Model:

r(P) = r(Q) (a=0, b=l)

Model: r(P) = 0.9 + 0.7r(Q)

(a=0.9, b=0.7)

Factory C Model:

r(P) = 0.6 + 0.8r(Q) (a=0.6, b=0.8)

Model: r(P) = 0.3 + 0.9r(Q)

(a=0.3, b=0.9)

Model: r(P) = 0.6502 + 0.9567r(Q) (a=0.6502, b=0.9567) Model: r(P) = 0.2865 + 0.9795r(Q) (a=0.2865, b=0.9795)

191

4.3.2.4.2 Residual Plots

4.3.2.4.2.1 Plots: Residuals Against r(0) - Check the linearity and Constant

Variance. Figures 4.5 exhibits the residual plots ofthe residuals of r(P) against the

ranks of quality r(Q) in all cases. By visual inspection, all these plots have no

evidences showing that these models are not linear or have no constant variances.

Restdual Plot: e * r(Q)

0.5 +

CO 0

S -0.5 1 OC

-1 + -1.5

4

r(Q)



1

0.5

ra 0 3 •g -0.5 1 OC

-1

-1.5

4

•

r(Q)


0.8

5 0.6 •o w 0.4 » • 0.2

n

( ) 2 4 6

r(Q)



1

0.5

0 -J2 ra 3 "O •« -0 5 -OC

-1 +

-1.5

r(Q)

Gingham (Factory C, ABC Company) Piece-dyed Fabric (Factory A, ABC Company) (c) (d)

Figure 4.5 Residual Plots: Residuals Against Ranks of Quality

192


_j2 ra 3

•o 'vi «

OC

1.5

1

0.5

0 -

-0.5 i'

-1 -

—1

4 •

r(Q)


(e)


1

0.5

1 0

"5! -0 5 T OC

-1 + -1.5

\

r(Q)


(0


6

4 jrt 2 ra

^ -2? -4

-6

• •

• •

• •

^ ^ ^ I ^ — ^ ^

i(f 20 CD

r(Q)



2 + "5 I 0 «A «

" -2 +

-4

• •

• • • 1 0 * « 0 3D

r(Q)



193

4.3.2.4.2.2 Plots: Residuals Against Time - Check the Nonindependence of

Error Terms. Figures 4.6 displays the residual time plots ofthe residuals of r(P)

against the time sequence, r(T) for all cases. These residual time plots fail to show

evidences to conclude that the error terms are nonindependent.


1 -^

0.5 (A

ra 0

2 -0.5' OC

-1

-1.5

1 2 4 (

r(T)

r(T)

1



1

0.8

S 0.6 •o

•«» 0.4 « • 0.2

n -

r(T)

0 2 4 6

r(T)



0.5 vt ra 0

2 - 0 . 5 ; oc

-1

-1.5

4

•

r(T)



1

0.5

ra 0 2 ( « -0.5 ' « OC

-1 1 c

•

• • T 1 2 4 1

•

i

r(T)


(d)

Figure 4.6 Residual Time Plots: Residuals Against Time Sequence

194


J2 ra 3

"35 «

OC

2

1.5

1

0.5

0

-0.5

-1 • i * i;

r(T)


(e)


0.5 J2 ra

2 -0.5 OC

-1

-1.5

r(T)


(f)


V) ra

6

4

2

0 2

^ -2l|l

-4

-6

• •

• • •» # : >

10 2 0 * 30

r(T)


Residual Time Plot: e * r{T)

ra 3

« 0

4

2

0

-2

• » I ^ • t

1 0 * • 2 0 ^ 3P • • •

r(T)



195

Further confirmation by using the Durbin-Watson test are needed for the two

complicated plots. Figures 4.6(g) and (h). Table 4.28 summarizes the test results by

using this method. The results indicate that the error terms in these two cases are

both noncorrelated with time. That means the ranks of data are independent of time.

Table 4.28 The Durbin-Watson Test Results for the Quality-Productivity Relationship of PNP and Token Ring Cases

HQ: Data are independent wdth time

Hi: Data are nonindependent with time

Significance level a = 0.05

Cases Results

PNP

Token

Ring

Critical region (n=29): dL=1.34, du=1.48 n n

Computed data: Z(^, "^/-i)' =490.7562, X ^ / = 172.1852, t=2

D =

/=i

lL(e,-e,J t=2

n 2.850

Conclusion: Since D > du, accept Ho


Computed data: Y.{e, - e,_, f = 144.0387, X^,' = 67.31445, /=2

D =

/=i

Y.(e,-e,J t=2

t=\

= 2.140

Conclusion: Since D > du, accept HQ

196

4.3.2.4.2.3 Plots: Residuals Against Expected Values - Check the Normaliy

of Error Terms. Figure 4.7 exhibits the normal probability plots for residuals ofthe

specific models. Because the residuals and MSE are all zeros in the case of gingham

in Factory B of ABC Company, its error terms is exactly subjected to normality since

there is only one point in the plot. This plot is not included in the Figure 4.7.

Normality Plot: e * EXPVALUE Normality Plot: e * EXPVALUE

M ra 3 "O

Q£

1

0.5

0 1

« ^ ( -U.b

-1

- 1 . 5 J

1 0.5

•

•

EXPVALUE

(A ra 3 12 tn 0) OC

0.5

n ^ ^ (

-O.b

-1

- 1 «; -

,

0.5

•

•

EXPVALUE

Gingham (Factory A, ABC Company) Gingham (Factory C, ABC Company) (a) (b)

Normality Plot: e * EXPVALUE Normality Plot: e * EXPVALUE

1

0.5 +

0 jn ra 3

•g -0.5

-1 +

-1.5

0.5

EXPVALUE

ra

3

0)

OC

1.5 1

0.5

0 -

-0.5 <»

-1 -

0.5 ^4^

EXPVALUE

Piece-dyed Fabric (Factory A, ABC Company) Piece-dyed Fabric (Factory B, ABC Company)

(Cl (d) Figure 4.7 Residual Plots: Residuals Against Expected Values

197


1

0.5 +

0 J2 ra 3 "D S -0.5 T oc

-1 + -1.5

.•e 0.5 1

EXPVALUE


(e)

Normality Plot: e * EXPVALUE 6

4

tn 2 ra

I 0 oc -2\

-4

-6

/

/ ^

•

•

EXPVALUE

PNP Ethernet Combo (XYZ Company) (f)

Normality Plot: e * EXPVALUE A ,

3

2 M

•o

t 0

-2

-3

•

• •

• 1 0.5 j r 1

EXPVALUE

5

Token Ring (XYZ Company) (g)


Except for Figure 4.7(d), other plots show reasonably close to straight line

form. The correlation coefficient of Figure 4.7(d) is 0.7, yvhich is not high enough to

conclude normality according to Looney and Gulledges' approach.

198

4.4 General Discussion

This section presents a discussion on the results of data analysis of section

4.3. This discussion includes the summarized statement, confidence level, and the

specific models of Quality-Profit and Quality-Productivity relationships.

Productivity-Profit relationship is discussed from the theoretical viewpoint. In

addition, several points regarding the data collected are also discussed.

4.4.1 Discussion of Quality-Profit Relationship

According to the results of hypotheses tests listed in Table 4.22, it is

acceptable to claim that product quality positively affects unit profit. Among the

eight cases, seven cases confirmed that the ranks of quality and unit profit have a

positive relationship through the hypotheses test. Only one case, piece-dyed fabric in

Factory A of ABC Company, failed to confirm this positive relationship. However, in

this case, it does not mean that this relationship is negative or irrelevant. From the

statistical viewpoint, when a hypothesis test fails to reject the null hypothesis, it

simply means there is not sufficient evidence based on sample data to accept the

alternative hypothesis. In fact, the correlation coefficient of this failed case is 0.4,

which also shows positive relationship between quality and unit profit; however,

based on sample data, this statement failed to be proved.

The smallest coefficient of correlation of population between the ranks of

quality and unit profit, based on the eight cases, is 0.7339. This number which was

199

calculated based on 95% confidence level came from the interval inference by

equation [4-3]. However, since this coefficient cannot exceed one, the confidence

level can be reduced. In equation [4-5], the required confidence level for the largest

p, 1, is 75%.^^ At this confidence level, the left-hand side p is 0.8154. This number

reveals a high correlation between the ranks of quality and unit profit.

The results ofthe specific models analyzed (section 4.3.2.2) shows that, all

models are applicable except the case of piece-dyed fabric in the Factory A of ABC

Company. The observations and predicted values of unit profit based on the specific

models are tabulated in the Appendix G. Note the predicted unit profits ofthe four

cases, gingham in the three factories and piece-dyed fabric in Factory A, exactly fit

the models. Hence, the predicted value is exactly the same as the observed data.

4.4.2 Discussion of Productivity-Profit Relationship

Theoretically, according to the equation [A-21] of Appendix A, the

productivity is directly related to unit profit. This is because productivity and unit

profit are such defined that they relate with each other. However, there are still two

variables that affect this relationship, i.e., total cost I and production quantity V. One

important assumption ofthe model development of this research is based on "when

quality is enhanced, unit cost, W, decreases or at least does not increase."

" According to equation [4-3], if the right-hand side equals one, taa must be 1.2557. That means the cumulative probability for 1 - a/2 is 0.875.

200

According to [A-21], when quality increases, unit profit increases as productivity

increases.

There are three reasons for the assumption, "the enhancement of quality will

decrease or not increase the unit cost." First, the decreases in defective products or

rework reduces costs and hence, increase revenue. Second, overhead costs are

reduced due to the more stable process. Third, the benefit from larger sales reduces

unit cost. Therefore, nearly all researchers, such as Deming (1986), Juran (1993),

Feigenbaum (1983), Crosby, P. B. (1979), maintain that enhanced quality must

decrease costs. Therefore, the pursuit of higher product quality is encouraged.

The test results ofthe field data listed in Table 4.23 demonstrates the high

correlated relationship between productivity and unit profit. In theory, it should

exactly correlate, but the test ofthe field data does not show this exact relationship.

This is due to the discrepancy between the assumption just mentioned and physical

data. There are two potential causes for this discrepancy: the assumption is fallacious

or the field data collected is incorrect. However, since many researchers assert that

higher quality will reduce cost and this research agrees, the only possible cause is the

field data. Perhaps, this is another topic for the interested researchers to conduct a

long-term confirmatory study to clarify the relationship between quality and

production cost.

201

4.4.3 Discussion of Quality-Productivity Relationship

According to the results of hypotheses tests listed in Table 4.24, it is

acceptable to claim that product quality is positively related to productivity. Among

the eight cases, seven cases confirmed that the ranks of quality and productivity have

a positive relationship through the hypotheses test. Only one case, piece-dyed fabric

in the Factory B of ABC Company, failed to confirm this positive relationship at

confidence level 95%. However, if confidence level is reduced to 90%, the

conclusion ofthe hypothesis test changes to accept the alternative hypothesis. This

result shows that a positive relationship between the ranks of quality and productivity

exists, which also indicates that quality and productivity is positively correlated.

The coefficient of correlation of population between the ranks of quality and

productivity, based on the eight cases, could be higher than 0.7923. This number

shows the ranks of quality and productivity positively correlated with at least 0.7923

coefficient based on 95% confidence level. This number reveals a high correlation

between the ranks of quality and productivity. Therefore, it is satisfactory to claim

that quality and productivity are positively correlated.

The results ofthe specific analyses of models presented in section 4.3.2.4

show that, all models are applicable except the case of piece-dyed fabric in the

Factory B of ABC Company. The observations and predicted values ofproductivity

based on the specific models are tabulated in the Appendix H. The predicted

202

productivity ofthe product gingham in the Factory B, exactly fit the models. Hence,

the predicted value is exactly the same as the observed data.

The case that failed to fit the model, piece-dyed fabric in the Factory B, is due

to the nonnormality of its data. Because the sample size is not large, one outlier may

severely influence the resuh. It is reasonable to suspect the upper point in Figure

4.7(d) might be an outlier; however, without sufficient evidence, no further action

can be done to disregard this point.

4.4.4 Discussion of Data

There are three problems regarding the data of this field research which must

be addressed. These problems influence the results of data analysis.

The first problem lies in the sample size, especially in the ABC Company.

Although in each case ofthe ABC Company there are only five sample data, five of

the six cases confirm the positive relationship. In the two cases of XYZ Company,

both sample sizes are much larger, also verify this relationship. Based on these

results, the confirmation is, in general, satisfactory.

The second problem of this field study is about the quality conformance level.

Three points regarding this problem need to be noted: (1) The data of quality

conformance level is converted from the original data, which is not measured in %;

(2) Different products have different quality criteria; therefore, conformance level has

different meanings for different products; (3) These values of quality data (%) are

203

very close. Due to this fact, using the concept of ranks may be a better way to

compare with productivity or profit.

The third problem regarding the relationships of Quality-Profit, Productivity-

Profit, and Quality-Productivity concerns the data of production quantity. Because

quantity affects cost, revenue, and profit, it must be taken into account when attempt

to relate quality, profit, and productivity. This is the reason that unit profit, instead of

profit, is used through this research.

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CHAPTER 5

CONCLUSIONS AND RECOMMENDATIONS

This chapter summarizes this research, presents further discussion and

conclusions, and provides recommendations for the future research. The summary,

presented in section 5.1, briefly illustrates the features and contributions of this

research. Section 5.2 gives further discussion and implications which are not

mentioned in the previous chapters. Conclusions are summarized in several points to

highlight the applicability of this research and is addressed in section 5.3. In the last

section, 5.4, recommendations for the future research are proposed from both the

theoretical and practical standpoints.

5.1 Summary

This research investigates the relationships of Quality-Profit, Productivity-

Profit, and Quality-Productivity. The Quality-Productivity relationship is a

controversial topic, especially prevalent in the manufacturing industries. In order to

realize this relationship, it is better to connect them with an intermediate variable.

This research believes the best intermediate variable is profit because it is one of

management's main concerns. Therefore, at first, it is essential to understand the

relationships between quality and profit, and productivity and profit. However,

205

because profit is affected by sales quantity, it is better to choose the unit profit to

compare with other variables.

Most ofthe literature review of this research demonstrates that the Quality-

Productivity relationship should be positive; however, few of them could prove this

assertion. The few who presented their mathematical models had several key

concepts that were not clarified: (1) quality cost was synonymous with production

cost, (2) no mention ofthe influence of sales quantity, (3) quality conformance level

(%) was regarded as an interval or ratio scale of measurement, (4) no explanation of

how quality could be measured to get unit of measure in %.

In order to improve these deficiencies ofthe current models regarding

Quality-Productivity relationship, this research utilizes the concept of ranks to relate

variables based on unit profit. In addition, the cost used in this research is production

cost, not quality cost, which is difficult to accurately measure under the current cost

accounting system used by most industries.

This research investigates the relationships of Quality-Profit, Productivity-

Profit, and Quality-Productivity in two ways: theoretical and practical. The

theoretical models of Quality-Profit, Productivity-Profit, and Quality-Productivity

relationships are summarized in Table 5.1. For detailed development of these models

refer to Appendix A. These models are developed so that they are generic to

manufacturing environments. These three models show that the three relationships

are all positively correlated.

206

Table 5.1 Summary of Mathematical Models of This Research

Relationship

Quality-Profit

Productivity-Profit

Quality-Productivity

Model

r(Pu) = a, + b,r(Q),

Zr(Qi)r(Pui)-n(n+l)V4

bi = - 4 , Z[r (Q.) ] ' -n(n +1)^/4 i = l

ai = (l-b,)(n+l)/2.

Pu = ( P - l ) x ^

r(P) = a2 + b2r(Q)

Zr(Q.)r(P,)-n(n +1)^/4

Z [ r ( Q . t f - n ( n + l ) V 4 i = l

a2 = (l-b2)(n+l)/2.

In the field study part of this research, two companies in Taiwan were

selected to confirm the relationships. The analysis of field data verified the

207

alternative hypotheses that all three relationships are positively related. In addition,

specific models for the investigated cases were also presented in Tables 4.25 and

4.27. By model analysis, most ofthe specific models are suitable to the cases. This

result makes firm the belief that there must be a positive relationship between quality,

unit profit, and productivity.

5.2 Further Discussion and Implications

Section 5.2.1 addresses some issues that need to be further discussed.

Besides, section 5.2.2 presents implications of this research. These implications

extend the explanations for the results of this research.

5.2.1 Further Discussion

There are two key assumptions in the model development of this research in

Appendix A. One assumption is, "all conformed goods could be sold." In the real

world, whether all conformed goods can be sold is questionable. This problem

involves pricing strategy, product innovation, and other factors such as damage

caused by storage, shipping and handling. However, due to the difficulty of

measurement, these factors are not taken into account in the models.

The other assumption, "that unit cost will not increase when quality

improves," was asserted by most researchers. Based on this assertion, quality

improvement is encouraged; otherwise, the question arises as to whether it is

208

profitable to improve product quality. Therefore, this assertion becomes an important

statement of this research.

In addition to the assumptions addressed above, there are two other important

variables that affects the relationships of quality, profit, and productivity, not

addressed in this research. These two influential factors are marketability and

production capacity. Even though the PIMS has proved in practice that better quality

results in bigger market share, and hence, produces more profit, this research handles

this factor as a constant. This means, in fact, the profit that will be created is higher

than the estimated value ofthe proposed model of this research. Therefore, models

of this research are conservative in estimating profits.

Production capacity is also considered satisfactory when relating the variables

of quality, profit and productivity. The better product quality will "pull" more

demand from market, and then "push" the necessity of expanding production.

Therefore, in this research, capacity as assumed can increase with the demand

v^thout difficulty.

5.2.2 Implications

The implications of this research includes the following points:

1. Even though the product quality is not measured in conformance level (e.g.,

measured in defects per one hundred pieces), according to rank, the model

is still appHcable.

209

2. Models that failed to be applied can possibly be remedied by methods, such

as enlargement of sample size, adding weights to data (e.g., different

weights for different lots), transform nonlinear regression into linear, or

examine the questionable data to exclude the outliers, etc. To remedy the

two cases in which models are not apt to use would be meaningless because

the sample size is too small.

3. If the relationship between two variables is categorized into five classes

according to its correlation coefficient:

• Exactly correlated p = I

• Highly correlated 0.67 < p < 0.99

• Mediumly correlated 0.34 < p < 0.66

• Low correlated 0.01 < p < 0.33

• Exactly independent p = 0

then, the relationships of Quality-Profit, Productivity-Profit, and

Quality-Productivity in the investigated companies could be classified as

highly correlated.

4. This research strongly suggests that the relationships of Quality-Profit and

Quality-Productivity from the viewpoint of improving quality is positively

related. That is, if quality is improved, then unit profit and productivity

should increase. However, if the assumption of unit cost changed, from

"not increase" to "not decrease," the results of this research are still

210

applicable. That is, when quality is lowered, the unit profit and

productivity should also decrease.

5.3 Conclusions

Conclusions of this research are summarized in the following points.

1. The proposed mathematical models of this research were validated through

the field study.

2. Although the positive relationships were verified by the ranks, it also

shows that the variables for quality, profit, and productivity are positively

related.

3. The result of this research supports the concept of kaizan (continuous

improvement). That is, the more improvement in quality or productivity,

the more profit will be created.

4. Specific models based on ranks could be established and verified in other

cases where definitions of quality, productivity, and profit may differ from

this research.

5. That quality must be measured in conformance level is not necessary.

When in application, the model only needs the ranks of quality. Therefore,

this model can be applied more yvddely.

211

6. Although the specific models are only suitable to the investigated

companies, the approach to link variables as well as the mathematical

models are believed to be genenc to all industries.

5.4 Recommendations

Recommendations regarding this research are separated into two parts,

theoretical and practical recommendations. These are addressed next respectively.

5.4.1 Theoretical Recommendations

To the researchers who are interested in studying further the relationship

between quality and productivity, this research recommends that the follov^ng issues

be taken into account.

1. Besides the nonparametric statistical approach, there may exist other

approaches to connect the quality, profit, and productivity. However, be

cautious of whether the data are of interval or ratio scales of measurement.

2. Quality, profit, and productivity may be defined in different ways; however,

they must be operationally defined such that the relationships between them

can be clearly understood.

3. Further exploration on the relationship between quality and productivity

based on quality cost may be feasible; however, the relationship between

quality cost and production cost must be first clarified.

212

5.4.2 Practical Recommendations

The purpose of studying the relationships of Quality-Profit, Productivity-

Profit, and Quality-Productivity is to ensure management that the enhancement of

quality and productivity will create higher profit. In order to reach this, the following

steps are suggested:

1. Define clearly the terms used for desired performance measures. Different

definitions may result in totally different performance index.

2. Develop specifically the steps to measure the performance index.

3. Implement strictly according to the steps for measuring the required data.

4. Develop models based on the observed data and predict values for future

control.

5. Examine the models by its assumptions.

6. Amend models if more data are collected.

7. During the process of measuring performance, identify the affecting factors

and try to improve them.

8. Keep using this process to maintain continuous improvement on

performance.

213

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233

APPENDDC A

MATHEMATICAL MODELS DEVELOPMENT

234

A.l Model Development for The Quaiity-Proflt Model

Let I: Total input ($)

R: Total revenue ($)

PT: Total profit ($)

Pu: Unit Profit


V: The volume produced

VQ: Volume of quality conformed

VB: Volume of quality nonconformed.

Therefore,

PT = R - I [A-1]

V V Q = ^ = ^ ^^ , 0 < Q < 1 , V>0 [A-2]

Pu = Y = ^ , V>0. [A-3]

Assume the increase in Q results in the decrease (or at least no increase) in

Unit I (i.e., lA^), [A-3] shows the larger RfV, the larger Pu- Suppose that all quality

conformed products can be sold, then the larger VQ, the larger R.

That is, if Q increases, then

and

235

R oc VG . [A-5]

Since V is positive, [A-5] can be expressed as

R V^

According to [A-2] and [A-4],

Pu °c Q . [A-7]

Now that the higher Q, the larger Py , these two variables are monotonically

and increasingly related. According to Conover (1980), the ranks of Pu and Q must

have a linear relationship.

Denote: r(Pui): the ith rank of Pu in an ascending Pu series

r(Qi): the ith rank of Q in an ascending Q series

n: number of paired data.

The linear relationship between r(Pu) and r(Q) is expressed by [A-8].

r(Pu) = ai + b,r(Q) [A-8]

where.

nZr(Q;)r(Pu,)-Zr(Q,)Zr(Pui) i=] i= l_

nZWQ,)f-[Zr(Q,rf b, = ^ = ^ - ^ •^ '^ [A-9]

i=l

£r(Pu, ) I [ r (Q | )f - Zm, )Xr(Q, )r(P„) M M i=l

nZ[>-(Q,)]'-[Zr(Q,)r a, = "^ —„ —. . [A-10]

i = l i = l

236

Since

i:r(Q:) = Zr(P„,) = ^ [A-U] i = l i = l ^

substitute [A-11] into [A-9] and [A-10] respectively,

n

Zr(Q.)r(Pu.)-n(n + l ) V 4 i=l

II

Z[r (Q. ) ] ' -n (n +1)^/4 1=1

[A-12]

ai = (l-bi)(n+l)/2. [A-13]

[A-8] provides an important function of regression methods, i.e., to estimate

A

E(Pu Q = Qo), an estimated expected value of Pp at Q = Qo, or to estimate

A

E(Q Py = Puo), the estimated expected value of Q at Pu = Puo Conover (1980)

presents the procedure for estimation. For any given Qo within the observed range of an ascending Q series, i.e., Qi

A

< Qo < Qn, E(Pu Q = Qo) is estimated by the following steps:

(1) Calculate r(Qo)

r(Qo) = r(Q.) + | ^ f | ^ [ r ( Q ^ ) - r ( Q O ] [A-14]

where Qi and Qj are the two adjacent observed values in the ascending

Q series such that Q, < Qo < Qj.

Note the rank of r(Qo) is not necessary an integer.

237

* Do not calculate r(Qo) if Qo is less than the smallest observed Qi

or greater than the largest observed Qn.

(2) Calculate r(Puo)

r(Puo) is calculated by [A-8]. r(Puo) is not necessary an integer.

(3) Calculate E(Pu Q = Qo)

r(Puo)-r(P„i)

r(Pu,)-r(Pu.) E(Pu Q=Qo)-Pu,+:r. ::. :(Pu.-Pu.) [A-IS]

where r(Pui) and r(Puj) are the two adjacent values in the ascending

r(Pu) series such that r(Pui) < r(Puo) < r(Puj).

If r(Puo) is greater than the largest observed rank of Pun, let

A

E(Pu Q = Qo) = r(Pun)- If r(Puo) is less than the smallest observed

rank of Pui, let E(Pu Q = Qo) =r(Pui).

For any given Puo, E(Q P = Puo )is estimated by the folloyving steps:

A

(1) Calculate the two end points, the smallest E(Pu Q = Qj) and the largest

A

E(Pu Q = Qn), according to the preceding procedure.

(2) Calculate each r(Q,) for each r(Pui)

r(Q) = [r(Pu)-a, ] /b, [A-16]

This equation is another form of [A-8].

(3) Convert each r(Q,) to E(Q | P = P .)

238

r(Q, - r Q , E(Q P u = R , ) = Q , + • ^ ( Q , - Q ) [A-17]

v^ u u,; Vj r(Qj-r(Qj)^^' ^'^ ^

where r(Qj) and r(Qk) are the two adjacent ranks of observed Qj and

Qk such that r(Qj) < r(Q.) < r(Qk).

Note if r(Q,) is greater than the largest rank of observed Qn, or less

than the smallest rank of observed Qi, then no estimate

A

E(Q Pu = Puj) can be found.

A.2 Model Development for The Productivity-Profit Model

Let P denote the productivity, which is defined as a profit-based ratio of

valuable output to measurable input. Therefore, the productivity can be expressed as

R P = — , where R, P > 0; I > 0 [A-18]

or

R = P x I . [A-19]

By substituting [A-18] into [A-1], the total profit can be rewritten as

PT = P X I - I = ( P - 1 ) X I [A-20]

[A-20] divided by V, then

PU = ( P - 1 ) X ^ - [A-21]

239

[A-21 ] indicates that only a productivity value greater than 1, can create

profit. The break-even point is at P = 1. '

A. 3 Model Development for The Profit-Based Quality-Productivity Model

According to [A-21], Pu is positively proportional to P-1. That is, when Q

increases (i.e., I/V does not increase),

Pu oc P. [A-22]

By [A-7] and [A-22], it is obvious that Q is positively proportional to P. That

is, Q and P are monotonically and increasingly related. Therefore, r(P) and r(Q), the

ranks of P and Q in the ascending P and Q series, respectively, also have a linear

relationship.

r(P) = a2 + b2r(Q) [A-23]

where,

Zr(Q.)r(P.)-n(n + l ) V 4

b2 = —„ [A-24] Z[r(Qi)] ' -n(n + l ) ' / 4 1=1

a2 = (l-b2)(n+l)/2 [A-25]

and n is the number of paired data of Q and P.

' This result is different from Sumanth's (1994) conclusion. Sumanth shows that the breakeven point for total productivity is always less than one. This difference lies mainly on the different

Output Total cost + profit calculations for cost. Sumanth's Total Productivity TP = - = - — — — In his

Input Total cost + working capital model, working capital is always greater than zero; therefore, the break-even point of TP (at profit = 0) is always than one. In this research , total cost is regarded as identical with total input.

240

[A-23] shows there exists a positive and linear relationship between the ranks

ofproductivity and quality. This linear regression model provides an approach, based

on ranks, to predict productivity P (or quality Q) with a given value Q (or P). The

A

procedure of prediction is similar to the steps of estimating E(Pu Q = Qo) and

A

E(Q Pu = Puo) in the preceding Quality-Profit model.

More specifically, for any given Qo within the observed range of an ascending

A

Q series, E(P Q = Q ) is obtained by the following steps:

(1) Calculate r(Qo)

Using the equation [A-14] and its rule.

(2) Calculate r(Po)

r(Po) is calculated by [A-23]. r(Po) is not necessary an integer.

(3) Calculate E(P I Q = Qo)

r(Po)-r(P.) E(P I Q = Qo)= Pi + ,(p";_,(yj(Pi-Pi) [A-26]

where r(Pi) and r(Pj) are the two adjacent values in the ascending

r(P) series such that r(P,) < r(Po) < r(Pj).

If r(Po) is greater than the largest rank of observed Pn, let

E(P I Q = Qo) = r(Pn)- If r(Po) is less than the.smallest rank of

observed Pi, let E(P Q = Qo)=r(P,).

241

On the other hand, for any given Po, E(Q P = PQ ) is predicted by the steps

(1) Calculate the two end points, the smallest E(P Q = Q,) and the largest

E(P Q = Q ) according to the preceding procedure.

(2) Calculate each r(Q,) for each r(P,)

r(Q) = [r(P) - a2 ] / b2

This equation is another form of [A-23].

[A-27]

(3) Convert each r(Q,) to E(Q P = Pj)

- I rRQ. -r(QJ E(Q P = P.)=Q.+ • ^ ^ ( Q , - Q )

' ' ' rQ,)-r(Q^)^'^'^ ^^^ [A-28]

where r(Qj) and r(Qk) are the two adjacent ranks of observed Qj and

Qk such that r(Q) < r(QO < r(Qk).

Note if r(Qi) is greater than the largest observed rank of Qn, or less

than the smallest observed rank of Qi, then no estimate

E(Q P = Pi) can be found.

242

APPENDIX B

QUALITY INSPECTION POINTS IN ABC AND XYZ COMPANIES

243

Table B.l Inspection Points ofthe Selected Products in ABC and XYZ Companies

Company (Factory)

ABC Company (Factory A)

ABC Company (Factory B)

Inspection point

Tensile strength of yam

Water ratio exceed ±10% Color discrepancy Color fastness to crocking Color fastness to sweating Color fastness to washing Color fastness to dry washing Color fastness to light Color fastness to chloride bleach washing Color fastness to sublimation Color placement Beam weight Yam density

Appearance (rough, holes, twist, etc.)

Broken number of beam, cheese Tensile strength of Warping yam Sizing rate Shrinkage rate Longitude density Latitude density Spidery web

244

Table B.l (Continued)

Company (Factory)

ABC Company (Factory C)

XYZ Company

Inspection point

Sizing rate

Shrinkage rate Water ratio exceed ±10% Color discrepancy Color fastness to crocking Color fastness to sweating Color fastness to washing Color fastness to dry washing Color fastness to light Color fastness to chloride bleach washing Color fastness to sublimation Color placement

Design error (Failed in functional test) SMT defects Bum-in failure Broken Damaged by dirty (dust, hair, etc.) Materials (drilling holes)

245

APPENDIX C

TABLE FOR THE SPEARMAN'S RHO TEST

246

Table C l Quantiles ofthe Spearman Test Statistic (Source: Conover,1980, p. 456)

n

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

p=.900

.800

.7000

. 000 .5357

.5000

.4667

.4424

.4182

.3986

.3791

.3626

.3500

.3382

.3260

.3148

.3070

.2977

.2909

.2829

.2767

.2704

.2646

.2588

.2540

.2490

.2443

.2400

.950

.800

.8000

.7714

.6768

.6190

.5833

.5515

.5273

.4965 4780 .4593 4429 .4265 .4118 .3994 .3895 .3789 .3688 .3597 .3518 .3435 .3362 .3299 .3236 .3175 .3113 .3059

.975

.9000

.8286

.7450

.7143

.6833

.6364

.6091

.5804

.5549

.5341

.5179

.5000 4853 4716 4579 4451 4351 4241 4150 .4061 .3977 .3894 .3822 .3749 .3685 .3620

.990

.9000

.8857

.8571

.8095

.7667

.7333

.7000

.6713

.6429

.6220

.6000

.5824

.5637

.5480

.5333

.5203

.5078

.4963 4852 .4748 .4654 4564 .4481 .4401 .4320 .4251

.995

.9429

.8929

.8571

.8167

.7818

.7455

.7273

.6978

.6747

.6536

.6324

.6152

.5975

.5825

.5684

.5545

.5426

.5306

.5200

.5100

.5002

.4915

.4828 4744 .4665

.999

.9643

.9286

.9000

.8667

.8364

.8182

.7912

.7670

.7464

.7265

.7083

.6904

.6737

.6586

.6455

.6318

.6186

.6070

.5962

.5856

.5757

.5660

.5567

.5479

For n greater than 30 the appropriate quantiles of p may be obtained from

where X is the p quantile of a standard normal random variable obtained from the normal distribution

table. The entries in this table are selected quantiles w^ ofthe Spearman rank correlation coefficient

p when used as a test statistic. The lower quantiles may be obtained from the equation

The critical region corresponds to values of p smaller than (or greater than) but not including the appropriate quantile. Note that the median of p is 0.

247

APPENDK D

RESULTS OF THE LILLIEFORTS NORMALITY TESTS

248

CUH FREQ 1.8 T

Pail* Diffepences

. 5 •-

-3.8

DAT /

3.8

Figure D. 1 Normality Test for Quality-Profit Data of Gingham (Factory A, ABC Company)

CUH niEQ 1.8 T

Palp Diffennces

. 5 ••

3.8 -2.8

DATi /

3.8

Figure D.2 Normality Test for Quality-Profit Data of Gingham (Factory B, ABC Company)

249

CUH FREQ i.e T

Pair Differences

.5 -

-3.8 -2.0

MTi i

3.8

Figure D.3 Normality Test for Quality-Profit Data of Gingham (Factory C, ABC Company)

CUn FREQ 1.8 T

Paip Diffepences

.5 --

-3.8

DATi /

3.8

Figure D.4 Normality Test for Quality-Profit Data of Piece-dyed Fabric (Factory A, ABC Company)

250

CUN 1.8 n

.5 -

Q

-3

FREQ

.8

95X UCL

-2.8 1

-I1B

Paip Diffepences

/ /

/

/

rfST

73/. L\»L^^^-- '

1 i 1 8.8 1.8 2.'8

MT((

1 2 3.8

Figure D . 5 Normality Test for Quality-Profit Data o f Piece-dyed Fabric (Factory B , A B C Company)

CUH FREQ 1.8 T

Paip Diffepences

.5 -

-3.8

DAT /

3.8

Figure D.6 Normality Test for Quality-Profit Data ofPiece-dyed Fabric (Factory C, ABC Company)

251

CUH FREQ 1.8 T

Paip Differences

.5 -.

-3.8

DAT /

3.8

Figure D.7 Normality Test for Quality-Profit Data of PNP Ethernet Combo

CUH FREQ 1.8 T

Paip Differences

.5 "

DAT I

3.8 -2.8 -1.8 3.8

Figure D.8 Normality Test for Quality-Profit Data of Token Ring

252

CUH 1.8 1

.5 -

Q

-3

FREQ

.8

m UCL

-2.8

/

1 y -IIB

Pair 1 )iffepences

/

m^

7 0 / . L\^L^_-—1 •-

1 1 1 8.'8 l.'e _2.'8

DATll

1 2 3'. 8

Figure D.9 Normality Test for Productivity-Profit Data of Gingham (Factory A, ABC Company

CUH FREQ 1.8 T

Paip Diffepences

.5 "

-3.8 I Z

Figure D. 10 Normality Test for Productivity-Profit Data of Gingham (Factory B, ABC Company)

253

CUH FBEQ 1 . 8 T

Pair Diffepences

.5 "

-3.8

DAT /

3.8

Figure D . 11 Normal i ty Test for Productivity-Profit Data o f Gingham (Factory C, A B C Company)

CUH FREQ 1 .8 T

Paip Diffepences

. 5 ••

-3.8

DAT i

3.8

Figure D. 12 Normality Test for Productivity-Profit Data of Piece-dyed Fabric (Factory A, ABC Company)

254

CUH FREQ 1.8 T

Paip Differences

.5 -

-3.8

DAT /

3.8

Figure D.13 Normality Test for Productivity-Profit Data of Piece-dyed Fabric (Factory B, ABC Company)

CUH FREQ 1.8 T

Paip Diffepences

.5 -•

-3.8

DAT /

-2.8 -1.8 3.8

Figure D. 14 Normality Test for Productivity-Profit Data of Piece-dyed Fabric (Factory C, ABC Company)

255

CUH FREQ 1.8 T

Pair Differences

. 5 ••

8 -3.8

DAT /

3.8

Figure D. 15 Normality Test for Productivity-Profit Data of PNP Ethernet Combo

CUH FREQ 1.8 T

Pair Differences

.5 "

DAT /

- ^ - 3 . 8 -2 .8 -1 .8 3.8

Figure D. 16 Normality Test for Prodctivity-Profit Data of Token Ring

256

Figure D. 17 Normality Test for Quality-Productivity Data of Gingham (Factory A, ABC Company)

CUH FREQ 1 Q ^ 1 .0 "

. 5 •

8 -3

95>: UCL

.8 -2'. 8

/

1 J

lie

Pi

/

lir Differences

/ NORjHrfST

/ 95Z I ri . \ » L j _ , ^

1 1 1 8.8 1.8 2.8

DAT/

1 2 3.8

Figure D. 18 Normality Test for Quality-Productivity Data of Gingham (Factory B, ABC Company)

257

CUH FREQ 1.8 T

. 5 •-

-3.8

DATi /

3.8

Figure D. 19 Normality Test for Quality-Productivity Data of Gingham (Factory C, ABC Company)

CUH FREQ 1 B T-1 . D

.5 -

8 -3 .8

95/. UCL

-2.8

Pair Differences

/ NOT

/ /

, _ i

y / /

»M

3J/. LLL^-—1 ^

/ 1 1 1

- l l8 8.8 l.'e 2.8

mi

1 2 3.8

Figure D.20 Normality Test for Quality-Productivity Data of Piece-dyed Fabric (Factory A, ABC Company)

258

CUH FREQ 1.8 T

.5 -

-3.8

Pair Differences

DAT /

3.8

Figure D.21 Normality Test for Quality-Productivity Data of Piece-dyed Fabric (Factory B, ABC Company)

CUH FUEQ 1 fl ^

. 5 •

8 -3 .8

95X UCL

-2 .8 1 /

-lie

Fair Differences

^

y

NOBH

/

m

95Z L C L ^ ^ ^

1 1 1 8.8 1.8 J.'8

mi

1 2 3.8

Figure D.22 Normality Test for Quality-Productivity Data of Piece-dyed Fabric (Factory C, ABC Company)

259

CUH FREQ 1.8 T

Pair Differences

.5 --

-3.8

DAT /

3.8

Figure D.23 Normality Test for Quality-Productivity Data of PNP Ethernet Combo

CUH FltEQ 1.8 T

Pair Differences

. 5 ••

8 -3.8 -2.8

DAT /

3.8

Figure D.24 Normality Test for Quality-Productivity Data of Token Ring

260

APPENDIX E

A PROOF FOR THE RELATIONSHIP BETWEEN SLOPE OF A REGRESSION

LINE BASED ON RANKS AND ITS CORRELATION COEFFICIENT

261

Let

X : independent variable.

Y: dependent variable

r(XO:theithrankofXi

r(Y,): the ith rank of Y,

n : number of paired data (X, Y).

According to Eqs. [A-8] and [A-12] in the Appendix A,

r(Y) = a + br(X) [E-1]

where

n

Zr(X.)r(Y.)-n(n +1)^/4 b = ^ ; . [E-2]

£ [ r (X . ) ] ' - n (n+1)^ /4 i=l

When sample data have no ties,

^ , ^ , n(n + l)(2n + l) Z[r(X. )f = Z[r(Y. )f = ^ . [E-3] i = l i = I "

Substitute [E-3] into [E-2],

12ir(X,)r(Y,)-3n(n + l ) '

n(n -1 )

On the other hand, according to Eq. [4-1] of section 4.3.1.1,

where

262

or

T = Z[r(X,)-r(Y,)f [E-6] i = l

=Z[r(X, )f - 2Zr(X. )r(Y,) +X[r(X)]') • [E-7] 1=1 i = l i = l

n 2 n 2

Again, replace Sr(X.) and XKYJ ) by [E-3], yields i = l 1=1

^^(A7 + l ) ( 2 ^ + l ) ^ , V N . V ^ T 22^r(X, )r(Y,)

i=l

i=l

Substitute [E-9] into [E-4],

[E-10] equals [E-5]. Therefore, b = p when there are no ties.

263

[E-8]

n

12Zr(Xi)r(Y,) = 2n(n + l)(2n+l)-6T . [E-9]

2n(n + l)(2n + l)-6T-3n(n + l)^ ' ' " n(n^-l)

= l - - 4 ^ [E-10] n(n -1)

APPENDIX F

THE DURBIN-WATSON TEST PROCEDURE AND ITS TABLE

264

1. Hypotheses:

Ho:p = 0

Hi:p>0, or Hi:p<0, or Ui'.Q^O

2. Given a significance level a ( 0.05 is used in this research)

3. Critical region: lower bound dL and upper bound du (obtained from the table listed

below).

4. Compute

D = -'^2__ [F-l] 1=2 n

t=l

where et is the residual at time t.

5. Decision:

IfD>du, accept Ho

IfD<dL, accept Hi

If dL < D < du, cannot decide.

265

Table F. 1 Durbin-Watson Test Bounds (Source: Neter, Wasserman, & Kutner,1990, p. 1140)

a = 0.05

n p - l = l * p - l = 2 p - l = 3 p - l = 4 p - l = 5

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 45 50 55 60 65 70 75 80 85 90 95 100

du 1.08

1.10

1.13

1.16 1.18

1.20

1.22 1.24 1.26 1.27

1.29

1.30 1.32 1.33 1.34

1.35 1.36 1.37 1.38 1.39

1.40 1.41

1.42 1.43 1.43 1.44

1.48 1.50

1.53 1.55

1.57

1.58

1.60

1.61

1.62 1.63

1.64

1.65

du 1.36

1.37

1.38 1.39

1.40 1.41

1.42 1.43 1.44

1.45

1.45 1.46 1.47 1.48 1.48 1.49 1.50 1.50 1.51

1.51 1.52

1.52 1.53 1.54

1.54 1.54 1.57

1.59 1.60

1.62 1.63 1.64

1.65 1.66

1.67

1.68 1.69

1.69

dL 0.95

0.98

1.02 1.05 1.08 1.10

1.13 1.15 1.17

1.19 1.21

1.22 1.24 1.26 1.27

1.28 1.30

1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39

1.43 1.46 1.49

1.51 1.54

1.55 1.57

1.59

1.60

1.61

1.62 1.63

du 1.54

1.54

1.54 1.53 1.53 1.54

1.54 1.54 1.54

1.55 1.55 1.55 1.56 1.56 1.56 1.57

1.57 1.57

1.58 1.58 1.58 1.59 1.59 1.59 1.60 1.60 1.62 1.63 1.64

1.65 1.66 1.67

1.68

1.69 1.70

1.70

1.71

1.72

du 0.82

0.86 0.90

0.93 0.97 1.00

1.03 1.05 1.08

1.10 1.12 1.14 1.16 1.18 1.20 1.21 1.23 1.24 1.26 1.27 1.28 1.29 1.31 1.32 1.33 1.34 1.38 1.42 1.45 1.48 1.50

1.52 1.54

1.56 1.57

1.59

1.60 1.61

du 1.75

1.73 1.71

1.69 1.68 1.68 1.67 1.66

1.66 1.66 1.66 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65

1.65 1.65 1.65 1.66 1.66 1.66 1.66 1.67 1.67

1.68 1.69 1.70 1.70

1.71

1.72 1.72 1.73

1.73 1.74

du 0.69

0.74

0.78

0.82 0.86 0.90 0.93 0.96 0.99 1.01

1.04 1.06 1.08 1.10 1.12 1.14

1.16 1.18 1.19

1.21 1.22 1.24 1.25 1.26 1.27

1.29 1.34 1.38 1.41 1.44

1.47 1.49

1.51 1.53 1.55

1.57

1.58 1.59

du 1.97

1.93

1.90 1.87

1.85 1.83 1.81 1.80 1.79

1.78 1.77 1.76 1.76 1.75 1.74 1.74 1.74 1.73 1.73 1.73 1.73 1.73 1.72 1.72 1.72 1.72 1.72 1.72 1.72 1.73 1.73 1.74

1.74 1.74

1.75 1.75 1.75

1.76

du 0.56

0.62

0.67 0.71

0.75 0.79 0.83 0.86 0.90

0.93 0.95 0.98 1.01 1.03 1.05 1.07 1.09

1.11 1.13

1.15 1.16 1.18 1.19 1.21 1.22 1.23 1.29 1.34 1.38 1.41 1.44

1.46 1.49

1.51 1.52

1.54 1.56 1.57

du 2.21

2.15

2.10

2.06 2.02 1.99

1.96 1.94 1.92

1.90 1.89

1.88 1.86 1.85 1.84 1.83 1.83 1.82

1.81 1.81 1.80 1.80 1.80 1.79 1.79

1.79 1.78 1.77 1.77 1.77 1.77

1.77

1.77 1.77

1.77 1.78

1.78 1.78

p-1 is the number of independent variables

266

APPENDDC G

PREDICTED VALUES OF SPECIFIC MODELS OF QUALITY-PROFIT

RELATIONSHIP

267

Table G.l Predicted Values of Specific Models of Quality-Profit Relationship

Case Gingham

(Factory A)

Model: r(Pu)=r(0) Gingham

(Factory B)

Model: r(Pu)=r(0) Gingham

(Factory C)

Model: r(Pu)=r(Q)

Piece-dyed Fabric (Factory A)

Model: r(Pu)=1.8+0.4r(Q) Piece-dyed Fabric

(Factory B)

Model: r(Pu)=0.3+0.9r(Q) Piece-dyed Fabric

(Factory C)

Model: r(PH)=r(Q)

Quality Q 0.978

0.9728 0.9633 0.9783 0.965 0.9786 0.9765 0.9816 0.975

0.9864 0.9683 0.968

0.9635 0.9762 0.9874 0.9791 0.9786 0.9751 0.9873 0.9755 0.9832 0.981

0.9853 0.975

0.9864 0.9778 0.9718 0.9653 0.9609 0.9808

r(Q) 4 3 1 5 2 3 2 4 1 5 3 2 1 4 5 4 3 1 5 2 3 2 4 1 5 4 3 2 1 5

Unit Profit Pu 17.70011 16.08827 14.38274 20.79271 15.42817 7.204602 6.535748 7.824846 5.333293 8.965322 -5.66707 -5.76316 -6.42779 -5.52866 -4.68155 11.09072 12.54258 11.18547 15.82587 11.22724 6.908694 5.095342 6.085383 4.573636 8.120502 -2.91604 -3.25962 -4.61092 -4.74119 -2.26657

r(Pn) 4 3 1 5 2 3 2 4 1 5 3 2 1 4 5 1 4 2 5 3 4 2 3 1 5 4 3 2 1 5

Predicted Pu' 17.70011 16.08827 14.38274 20.79271 15.42817 7.204602 6.535748 7.824846 5.333293 8.965322 -5.66707 -5.76316 -6.42779 -5.52866 -4.68155 11.7534 11.2273 11.1938 11.2795 11.21.5 6.0854 5.1943 6.8264 4.6780 7.8781

-2.91604 -3.25962 -4.61092 -4.74119 -2.26657

* The predicted values are obtained using equations [A-14] through [A-15] of Appendix A

268

T a b l e d (Continued)

Case

PNP

Model:

r(Pu)=0.3842

+0.9744r(Q)

Quality Q 0.9143 0.9032

0.9548 0.925 0.9438

0.9103 0.9317 0.9344 0.9298 0.9364 0.9387 0.9444 0.955 0.9448 0.9417 0.9519 0.942 0.9538 0.9569 0.9518 0.9483 0.9484 0.915 0.9531 0.9517 0.9587

0.9477 0.9532

0.9462

r(Q) 3 1 26 5 13 2 7 8 6 9 10 14 27 15 11 22 12 25 28 21 18 19 4 23 20 29 17 24

16

Unit Profit Pu 6.388036 5.099677 8.199355 6.7685 7.349688 5.367931 6.799667 6.849531

7.059123 7.09

6.899032 7.369683 8.371

7.607241 7.307667 8.23963 7.0898 9.73

9.549828 8.376964 8.17

8.099355 6.518667 8.739375 8.198793 9.678254 7.97

8.459032

7.787308

r(Pu) 3 1

21 5 13 2 6 7

9

11 8 14 23 15 12 22 10 29 27 24 19 18 4 26 20 28 17 25

16

Predicted Pu' 6.4282 5.1959 8.6604

6.7765 7.3507 5.7076 6.8597 6.9277

6.8112

7.0638 7.0898 7.3758 9.3007 7.6072 7.1123 8.2324 7.3109 8.4380 9.6355 8.1993 8.0894 8.1628 6.5891 8.3441 8.1951 9.7114

7.9606 8.3756 7.7827

"^

:v.ti

269 tE

I

Table G. 1 (Continued)

Case

Token Ring

Model:

r(Pu)=0.171 +0.9878r(Q)

Quality Q 0.9688 0.9567

0.9383 0.9394 0.96 0.9272 0.9653 0.952 0.9406 0.9364 0.9694 0.9613 0.9233 0.9208 0.9416 0.9308 0.9679 0.9294 0.9456 0.9233 0.9392 0.9706 0.9394 0.9281 0.9579 0.9594 0.9385

r(Q) 25

18 9

12.5 21 4 23 17 14 8 26 22 2.5 1 15 7 24 6 16 2.5 11 27 12.5 5 19 20

10

Unit Profit Pu 9.009938

7.182533 6.856417 6.155813 7.876333 5.219944 8.548067 7.0865

6.758875 6.109357 10.67978 8.0664

4.269533 3.387083

7 5.739667 8.67

5.4665 7.049438 4.98975 6.309917 10.46971 6.209529

5.3 7.389857 7.989611 6.129615

r(Pu) 25 18 14 10 20 4 23 17 13 8 27 22 2 1 15 7 24 6 16 3 12 26 11 5 19 21 9

Predicted Pu' 8.9643

7.1778 6.1312 6.5426 7.9799 5.2297 8.4951 7.0851 6.8564 6.1108 10.2557 8.0589 4.7308 3.5272 6.9982 5.7713 8.6551 5.4932 7.0482 4.7308

6.2132 10.6464 6.5426 5.3183 7.3772 7.8407 6.1584

^ ?&

270 ^

APPENDIX H

PREDICTED VALUES OF SPECIFIC MODELS OF QUALITY-PRODUCTIVITY

RELATIONSHIP

271

Table H. 1 Predicted Values of Specific Models of Quality-Productivity Relationship

Case Gingham

(Factory A)

Model: r(P)=0.6+0.8r(Q)

Gingham (Factory B)

Model: r(P)=r(Q) Gingham

(Factory C)

Model: r(P)=0.6+0.8r(Q) Piece-dyed Fabric

(Factory A)

Model: r(P)=0.3+0.9r(Q)

Piece-dyed Fabric (Factory B)

Model: r(P)=0.9+0.7r(Q)

Piece-dyed Fabric (Factory C)

Model: r(P)=0.3+0.9r(Q)

Quality Q 0.978

0.9728 0.9633 0.9783 0.965 0.9786 0.9765 0.9816 0.975

0.9864 0.9683 0.968

0.9635 0.9762 0.9874 0.9791 0.9786 0.9751 0.9873 0.9755 0.9832 0.981 0.9853 0.975

0.9864 0.9778 0.9718 0.9653 0.9609 0.9808

r(Q) 4 3 1 5 2 3 2 4 1 5 3 2 1 4 5 4 3 1 5 2 3 2 4 1 5 4 3 2 1 5

Productivity P 1.14098 1.141617 1.12875

1.156406 1.12661 1.136458 1.136433 1.149234 1.087342 1.176342 0.838504 0.775113 0.779061 0.817382 0.863716 1.151085 1.141617 1.12875

1.154797 1.12661 1.223801 1.136433 1.149234 1.087341 1.21949

0.857874 0.836848 0.796209 0.817381 0.90933

r(P) 3 4 2 5 1 3 2 4 1 5 4 1 2 3 5 4 3 2 5 1 5 2 3 1 4 4 3 1 2 5

Predicted P' 1.1415 1.1410 1.1275 1.1505 1.1312

1.136458 1.136433 1.149234 1.087342 1.176342 0.8174 0.7867 0.7767 0.8343 0.8536 1.1501 1.1416 1.1270 1.1541 1.1300 1.1492 1.1403 1.1984 1.1168 1.2212 0.8558 0.8368 0.8193 0.8004 0.8990

* The predicted values are obtained ""Model Development for The Profit Appendix A

according to the steps presented in the •Based Productivity-Quality Model" of

^

272 i

Case

PNP

Model:

r(P)=0.6502 +0.9567r(Q)

Table H. 1 (Continued) Quality Q 0.9143 0.9032

0.9548 0.925 0.9438 0.9103 0.9317 0.9344 0.9298 0.9364 0.9387 0.9444 0.955 0.9448 0.9417 0.9519 0.942 0.9538 0.9569 0.9518 0.9483 0.9484 0.915 0.9531 0.9517 0.9587

0.9477

0.9532 0.9462

r(Q) 3

1 26 5

13 2 7 8 6 9 10 14 27 15 11 22 12 25 28 21 18 19 4 23 20 29 17

24 16

Productivity P 1.370294 1.290575 1.517288

1.390082 1.435408 1.31207 1.41869 1.439059 1.427812 1.416324 1.40871 1.444761 1.539751 1.465235 1.466924 1.530221 1.437097 1.653459 1.628271 1.535214 1.527778 1.51687 1.398907 1.564924 1.49837 1.636681 1.517197 1.555784 1.483649

r(P) 3

1 20 4

10 2 8 12 9 7 6 13 24 14 15

22 11 29 27 23 21 18 5 26 17 28 19 25 16

Predicted P' 1.3806 1.3036

1.5606 1.4032 1.4465 1.3449 1.4171 1.4215 1.4117 1.4298 1.4358 1.4653 1.5953 1.4669 1.4374 1.5295 1.4398 1.5488 1.6319 1.5250 1.5145 1.5171 1.3943 1.5335 1.5173 1.6433 1.4971 1.5380 1.4829

.-.•« . . j ;

:^

273 tt3

Case

Token Ring

Model:

r(P)==0.2865 +0.9795r(Q)

Table H.l (Continued) Quality Q 0.9688 0.9567 0.9383 0.9394 0.96

0.9272 0.9653 0.952 0.9406 0.9364 0.9694 0.9613 0.9233 0.9208 0.9416 0.9308 0.9679 0.9294 0.9456 0.9233 0.9392 0.9706 0.9394 0.9281 0.9579 0.9594 0.9385

r(Q) 25 18 9

12.5 21 4 23 17 14 8 26 22 2.5 1 15 7 24 6 16 2.5 11 27 12.5 5 19 20 10

Productivity P 1.426808 1.340069

1.304051 1.274388 1.384956 1.230664 1.409745 1.308572 1.310594 1.275809 1.522488 1.374075 1.176205 1.1259 1.324374 1.237075 1.415031 1.244911 1.331262 1.210892 1.268964 1.508725 1.286928 1.229636 1.339293 1.388592 1.268367

r(P) 25 19

13 10

21 5 23 14 15 11 27 20 2 1 16 6 24 7 17 3 9 26 12 4 18 22 8

Predicted P' 1.4242 1.3386

1.2695 1.2960 1.3834 1.2298 1.4058 1.3308 1.3086 1.2684 1.4886 1.3880 1.2017 1.1393 1.3106 1.2483 1.4139 1.2384 1.3238 1.2017 1.2765 1.5188 1.2960 1.2318 1.3400 1.3699 1.2745

274

a study on the profit-based quality-productivity

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