taguchi based six sigma

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ORIGINAL ARTICLE

Taguchi-based Six Sigma approach to optimize plasma

cutting process: an industrial case study

Joseph C. Chen &Ye Li &Ronald A. Cox

Received: 19 September 2007 /Accepted: 10 April 2008 / Published online: 18 June 2008# Springer-Verlag London Limited 2008

Abstract This case study outlines the use of Taguchi

parameter design to optimize the roundness of holes madeby an aging plasma-cutting machine. An L9array is used in

a Taguchi experiment design consisting of four controllable

factors, each with three levels. With two non-controllable

factors included in the setting, we conduct 36 experiments,

compared to the 81 parameter combinations (four factors,

three levels or 34) required in a traditional DOE setting.

Therefore, using the Taguchi method significantly reduces

the time and costs of a quality improvement process.

Conducted for two response variablesbevel magnitude

and the smallest diameter deviation of the holethe

Taguchi experiments gave the optimal combination

A1B2C1D3 (small for tip size, 93 in/min for feed rate,

100 V for voltage, and 63A for amperage), which is

verified with a confirmation run of 30 work pieces. All 30

cuts meet the quality requirement for subsequent assembly.

Furthermore, statistical analysis indicates that the mean

value and standard deviation of the confirmation run data

are smaller than those before Taguchi parameter design is

conducted.

Keywords Taguchi method . Quality. Six Sigma .

Process optimization

1 Introduction

Many small- and medium-sized industries have imple-

mented the two most popular process improvement meth-

odologieslean manufacturing and Six Sigmawhich

originated at Toyota and Motorola, respectively. Each

methodology has its unique structure and tools. The central

focus of lean manufacturing is to provide value by

eliminating waste, which is defined as anything that is not

value-added from the customers perspective. The seven

deadly wastes, as defined by this method, are over-

production, inventory, waiting, movement, transportation,

defects, and over-processing. By continuously eliminating

these wastes, the customer receives a high value product.

When the variation of a part or a service does not meet the

specifications of the downstream internal and/or external

customers, the methodology and tools of Six Sigma can be

implemented to improve the quality of the product or

service. The latest structure of Six Sigma is defined as the

define-measure-analysis-implementation-control (DMAIC)

model. Each stage of the model provides tools for

conducting Six Sigma quality improvements for any

process or service.

Figure1 shows a summary of tools used in each stage of

Six Sigma management. In order to reduce the variation of

a process, many Six Sigma teams use design of experiments

(DOE) methodology to find solutions that will align

products with customer expectations. DOE is a statistical

Int J Adv Manuf Technol (2009) 41:760769

DOI 10.1007/s00170-008-1526-1

J. C. Chen

Department of Agricultural and Biosystems Engineering,

Iowa State University,

221 I. ED. II,

Ames, IA 50011-3130, USA

Y. Li (*)

Department of Industrial and Manufacturing Systems

Engineering, Iowa State University,

2019 Black Engineering,

Ames, IA 50011-2164, USA

e-mail: [email protected]

R. A. Cox

Center for Industrial Research and Service (CIRAS),

Iowa State University,

Campus, 2272 Howe Hall, Suite 2620,

Ames, IA 50011-2272, USA


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tool that studies the relationship between independent

variables, the Xs (process variables), and their interactions

on a dependent variable, the Y, which is considered the

critical-to-quality (CTQ) of the product.

The most commonly used DOE tool is the 2k factorial

design, where k is the number of factors, each with two

levels. Thus, in a three-factor design, there are eight

treatment combinations, i.e., 23 or 222. Unfortunately,

for most manufacturing processes, two levels of each factor

may provide insufficient information about quality im-

provement. Often, three levels for each factor are needed.

For example, when studying the feed rate of a turningoperation, three levels could be evaluated (e.g., 0.005,

0.010, and 0.015 in. per revolution). Thus, for a three-

factor, three-level design, there would be 27 treatment

combinations, i.e., 33 or 333. In addition, each treatment

combination should be run twice to achieve a more reliable

statistical data analysis, bringing the total number of

experiments to 54 (272). If the cost of each experimentis $100, the Six Sigma team will spend $5,400 to analyze

a three-factor, three-level experiment design with two

replicates.

In many manufacturing processes, achieving a solution

that meets customers specifications may require an

evaluation of five or six factors. Costs will increase

accordingly. For example, assuming a base cost of $100

per experiment, a six-factor, three-level experiment design

with two replicates will cost $145,800 (36 or 729

combinations2 =1,458). This is the cost of conducting

DOE alone and does not include time spent on DOE, which

may reduce the productivity of other jobs and delayresolution of the quality problem. In addition, during this

time, the process will produce more defects and wastes.

Based on the aforementioned analysis, resolving industrial

problems cost-effectively and in a timely manner requires a

Phase 0: Define

Scope and Boundary

Define Defects

Team Charterand Champion

Estimated $ Impact

Leadership approval

Phase I: Process Measurement

Map Process and Identify Inputs and Outputs

Cause and Effects Matrix

Establish Measurement System Capability

Establish Process Capability Baseline

Phase II: Process Analysis

Complete FMEA

Perform Multi-Vari Analysis

Identify Potential Critical Inputs

Develop Plan for Next Phase

Phase III: Process Improvement

Verify Critical Inputs

Optimize Critical Inputs via

Taguchi

Phase IV: Process Control

Implement Control Plan

Verify Long Term Capability

Continuously Improve Process

Fig. 1 DMAIC process improvement methodology

Fig. 2 Electric switchboard

Fig. 3 Plasma table

Fig. 4 Indicator light

Int J Adv Manuf Technol (2009) 41:760769 761


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more economical DOE approach. Taguchi parameter

design, which is capable of providing the optimal solution

with a reduced number of experiment runs, is one such

approach.

One small-sized, Midwest manufacturer has an aging

plasma-cutting machine that produces defects and causes

production delays. Though it is easier to replace older

equipment with new machines, most small manufacturershave limited capital. The manager of this company

approached the researchers for assistance in answering the

following questions:

1. What is the optimal setting to produce the highest

quality products?

2. Can the optimal setting lower the defect rate but

maintain the required productivity?

If the defect rate remains high after implementing

optimal settings, the manager will have the justification he

needs to invest in new equipment.

To address this challenge, the researchers conducted aTaguchi parameter design study, using the results of that

study to make recommendations. The procedure and process

is demonstrated in the four phases outlined in Fig. 1.

2 Overview of Taguchi parameter design

Taguchi parameter design is one of several methods

developed by Dr. Genichi Taguchi [1]. One of the

conventional approaches used in off-line quality control,

Taguchis philosophy is based on the belief that once

quality is designed into both the product and process, only

minimal inspection is necessary. Taguchi proposes a

holistic view of quality related to cost, which extends the

focus of quality beyond manufacturers at the time of

production by integrating the customer and society as a

whole. Taguchi defines quality as the (minimum) lossimparted by the product to society from the time the

product is shipped. This economic loss is associated with

losses due to rework, waste of resources during manufac-

turing, warranty costs, customer complaints and dissatis-

faction, time and money spent by customers on failing

products, and the eventual loss of market share. Taguchi

methods provide an efficient and systematic way to

optimize designs for performance, quality, and cost. These

methods have been used successfully in Japan and the

United States in designing reliable, high quality products at

low cost in such areas as automotives and consumer

electronics.Taguchi breaks down off-line quality control into three

stages, concept design, parameter design, and tolerance

design, which are summarized below:

Concept design results in either a design concept or an

up and limping prototype. In the initial phase, more

than one design concept, each with its own set of pros

and cons, can be presented. The ideal design concept

will be the one that research shows best addresses

customer needs and is inherently robust.

Bevel magnitudeFig. 5 Illustration of bevel

Smallest diameter deviation: |Dsmallet-Dnormal|

Dsmallest: Smallest diameter

Dnormal: Nominal diameter

Continuous curve: Actual plasma-cut hole

Dashed curve: Nominal diameter hole, maximal roundness

Dsmallest

D normal

Fig. 6 Illustration of smallestdiameter deviation

762 Int J Adv Manuf Technol (2009) 41:760769


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Parameter design is a critical production step. The

nominal design features or selected process factor

levels are tested and the combination of product

parameter levels or process operating levels leastsensitive to changes in environmental conditions and

other uncontrolled factors (noise) is determined.

Tolerance design is used to further reduce variation, if

required, by tightening the tolerance of those factors

shown to have a significant impact on variation. This

stage utilizes loss function to determine whether

spending more money on materials and equipment will

result in a better product, thus emphasizing the

Japanese philosophy of invest last not invest first.

Taguchi parameter design is an experiment-based pro-

cess that uses the following steps to identify settings ofdesign parameters that maximize performance character-

istics (e.g., yield or productivity, etc.):

1. Identify initial and competing settings of design

parameters, as well as important noise factors and their

ranges.

2. Construct the design and noise matrices, and plan the

parameter design experiments.

3. Conduct the parameter design experiments and evaluate

the performance statistic for each test run of the design

matrix.

4. Use the values of the performance statistic to predictnew settings of the design matrix.

5. Confirm that the new settings truly improve the

performance statistic.

Considering multiple factors simultaneously, the Taguchi

parameter design method uses orthogonal experimental

combinations to shorten the product development cycle,

which, in turn, saves time and money, Taguchi parameter

design has been utilized in traditional manufacturing

processes such as milling, turning, and drilling to determine

optimal combinations of parameters for better performance.

Ghani et al. [2] applied Taguchi parameter design to

optimizing parameters for end milling process. Low

resultant cutting force and good surface finish were foundwith high cutting speed, low feed rate and low depth of cut.

Zhang et al. [3] used a Taguchi parameter design

application to optimize surface quality in a CNC face

milling operation, where the best surface roughness

(response) and signal-to-noise ratio were sought. Davim

and Reis [4] studied cutting parameters of composite

milling process using Taguchi-based experiments. Kirby

et al. [5] discussed the application of Taguchi parameter

design to optimize turning operations for best surface

roughness. Palanikumar and Karthikeyan [6] used Taguchi

methods to conduct experiments in turning composite

material to achieve maximum material removal rate andminimum surface roughness. Taguchi parameter design has

also been used to analyze optimal parameters for drilling

process [7,8, 9,10].

Although many of the aforementioned projects were

conducted primarily in laboratories, research can also be

done in an industrial setting. The Iowa State University

Center for Industrial Research and Service (CIRAS), an

extension service unit of this Midwest land grant university,

Factor Units Level 1 Level 2 Level 3

A Tip Size - Small Medium High

B Feed Rate in/min 83 93 103

C Voltage volts (V) 100 105 110

D Amperage amperes (A) 43 53 63

Noise Low High

1 Air Pressure lbs/in2(PSI) 45 60

2 Pierce Time seconds (s) 0.70 1.40

Fig. 8 Test parameters

Fig. 7 Fish bone diagram



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has proposed this methodology to help industry to obtain

optimum manufacturing processes to meet customer

demands within a reasonable timeframe and budget. The

following sections will present the application of Taguchi

parameter design in helping a small business achieve the

Six Sigma paradigm.

3 Current problem with an older plasma-cutting

machine

The case study in this paper is based on a problem

presented by an electrical manufacturing company (Com-

pany A) located in Des Moines, Iowa. The major products

of Company A are large electrical switchboards (Fig. 2).

One step in the process of making the boards requires the

use of a plasma table (Fig.3) to cut holes for hardware such

as an indicator light (Fig. 4). The current problem of the

plasma cutting process is that some of the holes do not

allow the fitting for the hardware. A close examination of

the holes reveals that two reasons may keep the hardware

from passing through the holes. First, the plasma cutting

process is beveling the edge of the holes it creates (Fig.5),

which, in turn, obstructs the hardware. Meiji EMZ-5TR

zoom stereo microscope was used to measure the magni-

tude (unit: 0.001 inch) of the bevels for analysis. Second,

the holes have poor circularity (roundness). Roundness is

measured by finding the smallest diameter deviation, which

is the difference of the smallest diameter of the actual hole

from the nominal diameter (Fig. 6). Beveling and roundness

problems that prevent hardware from fitting properly into

the switchboard is a defect that requires rework. To

minimize production costs due to this rework, a Taguchianalysis was undertaken to determine the optimal setting to

produce holes with minimum bevel and minimum out-of-

round diameter. Ideally, all of the holes cut by the plasma

machine would have best round shape and enable the

hardware to be inserted smoothly.

To accomplish this project for Company A, a Six Sigma

team consisting of operators, engineers, researchers and a

manager was formed, and the Taguchi parameter design

procedure was applied.

4 Six Sigma improvement process

4.1 Define

4.1.1 Factors and levels

Before the Six Sigma team could conduct the Taguchi

parameter design experiment, they needed to thoroughly

Noise 1 2 3 4

45 45 60 60

0.7 1.4 0.7 1.4

Run A B C D Avg Bevel

1 1 1 1 1 39 31 22 42 33.5 8.96 80.33 -30.73

2 1 2 2 2 35 25 35 35 32.5 5.00 25.00 -30.31

3 1 3 3 3 55 19 32 37 35.75 14.91 222.25 -31.60

4 2 1 2 3 40 47 44 82 53.25 19.38 375.58 -34.94

5 2 2 3 1 40 52 62 87 60.25 19.97 398.92 -35.94

6 2 3 1 2 45 54 60 62 55.25 7.63 58.25 -34.91

7 3 1 3 2 52 48 49 49 49.5 1.73 3.00 -33.90

8 3 2 1 3 39 47 46 52 46 5.35 28.67 -33.30

9 3 3 2 1 56 51 40 45 48 6.98 48.67 -33.69

Noise Level Setting

S/N

Ratio

1-Air Pressure2-Pierce Time

N4

Control Factors and Levels

N1 N2 N32

Fig. 10 Data of bevel (unit:

0.001)

Noise 1 2 3 4

1-Air Pressure 45 45 60 60

2-Pierce Time 0.7 1.4 0.7 1.4

Run A B C D Avg Circularity

1 1 1 1 1 y11 y12 y13 y14

2 1 2 2 2 y21 y22 y23 y24

3 1 3 3 3 y31 y32 y33 y34

4 2 1 2 3 y41 y42 y43 y44

5 2 2 3 1 y51 y52 y53 y54

6 2 3 1 2 y61 y62 y63 y64

7 3 1 3 2 y71 y72 y73 y74

8 3 2 1 3 y81 y82 y83 y84

9 3 3 2 1 y91 y92 y93 y94

N1 N2 N3

Control Factors and Levels

Noise Level Setting

N4 2

Fig. 9 Taguchi experiment

table



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understand the plasma-cutting process. A brainstorming

exercise that examined all of the factors of the process

provided the necessary information. Since these factors

involve knowledge in different domains and could be either

controllable or non-controllable, it was necessary to have

all team members participate in the brainstorming. A

fishbone diagram based on this exercise revealed allpossible causes of defective plasma-cut holes from the

perspectives of method, material, machine, operator and

environment (Fig. 7). Through group discussion and

ranking, four factors were identified as controllable factors

(voltage, feed rate, amperage, and tip size) and two as

uncontrollable noise factors (air pressure and pierce time).

The Six Sigma team then determined ranges of the levels

to explore for each factor. For controllable factors, this was

done by determining normal settings for each factor and

then setting one level lower (level 1) and one level higher

(level 3), using the existing settings as level 2. For

uncontrolled factors (noise factors), two levels were chosen,

low and high. The levels and units of each factor are shown

in Fig. 8. These levels were set to determine if changes to

the factors impacted hole quality, and, if so, how much. In

this way, the most significant factor was identified, and theoptimal level for each factor determined. For the uncon-

trolled factors, the two levels helped determine if back-

ground noises produce a significant effect. This effect will

be further analyzed with T-tests.

4.1.2 Experimental design

Using these four controllable factors and two uncontrolled

noise factors, we constructed an L9 Taguchi experiment

table with the appropriate settings of each factor (Fig. 9).

For each controllable parameter setting combination, four

runs were conducted, each under a different noise factorsetting combination. Each trial run is represented as yij,

wherei ranges from 1 to 9, denoting controllable parameter

setting for experimental run, and j from 1 to 4, denoting

noise factor setting. Thus, a total of 36 experimental runs

are conducted as a setting shown in Fig. 9. The average

value, standard deviation, variance and signal-to-noise (S/

N) ratio of the four runs under the same controllable

parameter setting were calculated. The same experimental

28

36

44

52

60

-36

-35

-34

-33

-32

-31

-30

-29

-28

sm md lg

Factor A: Tip Size S/N Ratio

Ave Bevel

44

45

46

47

48

49

50

-37

-36

-35

-34

-33

-32

-31

83 93 103

Factor B: Feed Rate (ipm) S/N Ratio

Avg Bevel

42

44

46

48

50

52

54

-37

-36

-35

-34

-33

-32 100 105 110

Factor C: Voltage (Volts)

S/NR

atio

S/NR

atio

S/NR

atio

S/NR

atio

S/N Ratio

Avg Bevel

42

44

46

48

50

52

-37

-36

-35

-34

-33

-32 43 53 63

AvgBevel

AvgBevel

AvgBevel

AvgBevel

Factor D: Amperage (Amps)S/N Ratio

Avg Bevel

Fig. 12 Response graphs for bevel magnitude

Avg Bevel

A B C D Optima combinations(Raw Data)

level 1 33.92 45.42 47.25 47.25 smaller the better

level 2 56.25 46.25 44.58 45.75 A1, B1, C2, D3

level 3 47.83 46.33 48.50 45.00

S/N Ratio

A B C D Optima combinations(S/N Rati o)

level 1 -30.9 -33.2 -33 -33.5 larger the better

level 2 -35.3 -33.2 -33 -33A1, B2, C1, D2

level 3 -33.6 -33.4 -33.8 -33.3

Fig. 11 Response of controllable factors to bevel and S/N ratio



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design table was used for two response variables, the bevel

magnitude and the deviation of the smallest diameter of

plasma-cut holes.

4.2 Measure and analysis

This section provides details of the Taguchi-based experi-

ments conducted for bevel magnitude and smallest diameterdeviation. Data were collected and analyzed using the

experimental design described in the previous section.

4.2.1 Taguchi experiment for bevel

Figure10shows the experiment data for the bevel size. The

response of each controllable factor on bevel magnitude

and the signal-to-noise ratio are shown in Fig. 11. The

quality characteristic is the-smaller-the-better; the formula

to calculate S/N ratio is given below and its derivation can

be found in [1]:

h 10 log 1

n

X4j1

y2ij

!" #

where,

S/N ratio,

yij individual response for each trial run,

n the number of runs due to noise factors; in this case,

n=4.The bevel response table (Fig. 11) shows the mean

response of the variable (bevel) from each controllable

factor at each level in the Taguchi experimental design.

Each level of the controllable factors has three response

values in the orthogonal array (Fig. 10) and is calculated by

averaging these three values. The response table for the S/N

ratio (also in Fig.11) was similarly obtained, using the S/N

ratios in the orthogonal array. With the response values and

the S/N ratio values, the response table can be used to

determine the optimal combination of levels of the

controllable factors that creates the minimum bevel.

Figure12is the graphical depiction of the response and

S/N ratio for bevel magnitude. Since the quality character-

istic for beveling is the-smaller-the-better, the optimal

setting combination for minimum bevel is A1-B1-C2-D3,

which is interpreted as small tip size, a feed rate of 83 in/

min, a voltage of 105 V, and amperage of 63A. For the S/Nratio, we are looking for the largest value. Therefore, the

optimal setting combination for S/N ratio response is A1-

B2-C1-D2, which means small tip size, a feed rate of 93 in/

min, a voltage of 100 V, and amperage of 53A. The arrows

in Fig. 12indicate the chosen level of each factor, and the

directions of the arrows show the quality characteristic with

upward denoting the-larger-the-better and downward the-

smaller-the-better.

4.2.2 Taguchi experiment for smallest diameter deviation

Similarly, Fig. 13 shows the experiment data for thesmallest diameter deviation. The response of each control-

lable factor on the smallest diameter deviation and the S/N

ratio are shown in Fig.14. Figure15 is the graphic display

of the response to smallest diameter deviation. The quality

characteristic is also the-smaller-the-better for the smallest

diameter deviation. The optimal setting combination for

minimum smallest diameter deviation is A1-B2-C1-D3,

which means small tip size, a feed rate of 93 in/min, a

Fig. 14 Response of controllable factors to smallest diameter

deviation

Noise 1 2 3 4

45 45 60 60

0.7 1.4 0.7 1.4

Run A B C D

Avg

Bevel

1 1 1 1 1 0.002 0.007 0.018 0.020 0.012 0.0087 0.000075 37.116

2 1 2 2 2 0.001 0.001 0.006 0.016 0.006 0.0071 0.000050 41.337

3 1 3 3 3 0.006 0.001 0.003 0.019 0.007 0.0081 0.000066 39.925

4 2 1 2 3 0.012 0.018 0.021 0.052 0.026 0.0179 0.003200 30.442

5 2 2 3 1 0.037 0.044 0.060 0.055 0.049 0.0104 0.000109 26.0516 2 3 1 2 0.023 0.036 0.040 0.052 0.038 0.0120 0.000143 28.147

7 3 1 3 2 0.037 0.027 0.042 0.035 0.035 0.0062 0.000039 28.956

8 3 2 1 3 0.009 0.005 0.027 0.014 0.014 0.0096 0.000092 35.888

9 3 3 2 1 0.041 0.032 0.021 0.041 0.034 0.0095 0.000090 29.184

Noise Level Setting

1-Air Pressure

2-Pierce Time S/N

RatioControl Factors and Levels

N1 N2 N3 N42

Fig. 13 Data of smallest

diameter deviation (unit: inch)



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voltage of 100 V, and an amperage of 63A. The S/N ratio

responses render the same parameter setting combination.

4.2.3 Setting selection

According to Figs. 12 and 14, bevel and smallest diameter

deviation as well as their S/N ratios have different optimal

setting combinations. These are summarized in the first four

rows of Table 1. For example, bevel S/N ratio response

gave level 2 (53A) for factor D (amperage), while all other

responses (bevel, smallest diameter deviation and its S/N

ratio) chose level 3(63A). However, Company A needs

only one overall optimal setting combination for its plasma

table. Therefore, the appropriate optimal setting combina-

tion is the level of each factor having the largest number of

occurrences. For example, level 3 of factor D occurred

three times, while level 2 occurred once. Therefore, level 3

for factor D is chosen as the overall optimal setting

combination. With this rule, the overall optimal setting for

the plasma table is A1-B2-C1-D3, as indicated in the bottom

row of Table 1. The setting A1-B2-C1-D3 means the smalltip size, a feed rate of 93 in/min, a voltage of 100 V, and

amperage of 63A.

4.2.4 T-test

To examine the effect of noise factors on the response

variables, a t-test was conducted for each noise factor. For

-0.200

-0.150

-0.100

-0.050

0.000

0.050

24

26

28

30

3234

36

38

40

42

44

46

48

50

sm md lg

Factor A: Tip Size S/N Ratio

Deviation

0.0000.0050.0100.0150.0200.0250.030

0.0350.0400.0450.0500.0550.0600.0650.0700.0750.080

24

26

28

30

32

34

36

38

40

83 93 103

Factor B: Feed Rate (ipm)S/N Ratio

Deviation

-

-

2426283032343638404244464850

100 105 110

S/NR

atio

S

/NR

atio

S/NR

atio

S/NR

atio

Factor C: Voltage (Volts) S/N Ratio

Deviation

-0.020

-0.010

0.000

0.010

0.020

0.030

0.040

-0.020

-0.010

0.000

0.010

0.020

0.030

0.040

242628303234363840

42444648505254565860

43 53 63

D

eviation

D

eviation

Deviation

Deviation

Factor D: Amperage (Amps)S/N Ratio

Deviation

Fig. 15 Response graph for smallest diameter deviation

Table 1 Optimal setting combination

Selection Criteria Combination

Bevel A1 B1 C2D3Bevel S/N ratio A1 B2 C1D2Smallest diameter deviation A1 B2 C1D3Smallest diameter deviation S/N ratio A1 B2 C1D3Overall optimal setting A1 B2 C1D3

Table 2 T-test for air pressures effect on smallest diameter deviation

Air pressure (PSI) 45 60

Mean 0.019 0.030

Variance 2.4791 e-4 3.0446 e-4

Observations 18 18

df 34

Difference in mean 0.011

Std. Error (difference between the means) 0.0055

t Stat 2.0358

t Critical two-tail (alpha =0.005) 2.7284

P(T


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air pressure, a t-test determines if the two levels (45 psi and

60 psi) will have a significant effect on smallest diameter

deviation. The hypothesis is stated as

H0 : 45 60H1 : 456 60

The t-test result is shown in Table2. From the test result

it can be seen that the Abs (t Stat)=2.0358 < t critical two-

tail (alpha=0.005)=2.7284, or equivalently P (T alpha= 0.005. The statistical conclusion is

that the difference in mean from the two air pressure levels

is not significant, so the hypothesisHo can not be rejected.

Therefore, we can conclude that air pressure does not

significantly affect the smallest diameter deviation.

Similarly, three t-tests were conducted for the effects of

pierce time to smallest diameter deviation (Table 3), air

pressure to bevel (Table 4), and pierce time to bevel

(Table 5). From Table 3, it can be seen that the Abs

(t Stat)=0.6575 < t critical two-tail (alpha=0.005)=2.7284,

or equivalently P (T alpha=0.005.

Therefore, pierce time does not significantly affect the

small radius. From Table 4, it can be seen that the Abs

(t Stat)=1.2667 < t critical two-tail (alpha=0.005)=2.7284,

or equivalently P (T alpha=0.005.

Therefore, the air pressure does not significantly affect the

bevel magnitude. From Table 5, Abs (t Stat)=0.8738 < t

critical two-tail (alpha= 0.005) =2.7284, or equivalently P

(T alpha= 0.005. Therefore, the

pierce time does not significantly affect the small radius.

4.3 Implementation

After the overall optimal setting combination for the plasma

cutter was identified, a confirmation run was conducted.

With this optimal setting (A1-B2-C1-D3), 30 cuts were made

to test the smallest diameter deviation and the bevel

magnitude. The hardware passed easily through all 30 cuts,

meaning no rework was needed. In addition, as the results

shown in Table 6 indicate, the mean value and standard

deviation of the confirmation run data were smaller than

those before Taguchi design was conducted.

4.4 Control

The optimal setting combination was sent to Company As

production department. The Six Sigma team is now trying

to uncover other possible causes of unacceptable deviation

so that other Taguchi experiments can be conducted for

continuous improvement of the process. For example, if

defects occur later following the optimal condition, the Six

Sigma team will follow the DMAIC procedure (Fig. 1) to

pursue the next cycle of process improvement. Taguchi

Table 3 T-test for pierce times effect on smallest diameter deviation

Pierce time (s) 0.7 1.4

Mean 0.023 0.026

Variance 2.94 e-4 3.18 e-4

Observations 18 18

Df 34

Difference in mean 0.003

Std. Error (difference between the means) 0.0058

t Stat 0.6575

t Critical one-tail (alpha =0.005) 2.7284

P(T


10/10

parameter design for optimal condition could then be

executed again.

5 Conclusion

Six Sigma and lean manufacturing are powerful strategies

for transforming an enterprise and escalating its competi-

tiveness. The fact that Six Sigma and lean manufacturing

can successfully save time and cut costs are important

considerations, especially for small- and medium-sized

enterprises with limited resources. This paper presented

the application of the Taguchi method to optimize the

roundness of the holes cut by an aging plasma-cutting

machine. Using the orthogonal array in the experiment

design for four factors, the Taguchi method reduced the

experiment set-up from 81 parameter combination settings

(34) i n D O E t o an L9 setting. With two noise factors

included in the Taguchi experiment design, 36 total experi-

ments are conducted. The optimal setting combination

received from Taguchi experiment design is A1B2C1D3

(small for tip size, 93 in/min for feed rate, 100 V for voltage,

and 63A for amperage), which maintains the existing feed

rate for productivity and improves quality of products. The

optimal setting combination gave no defects from the 30

plasma-cut holes in the confirmation run. In addition, the

recommended setting combination was well received by

Company A, and the problem with defects situation has been

much improved. With the reduced time and cost, Taguchi

experiment design has again demonstrated its effectiveness

in achieving Six Sigma and lean paradigm.

Acknowledgement This project was partially funded by the Iowa

Center for Industrial Research and Service, through a grant from the

Department of Commerce NIST Manufacturing Extension Partnership.

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