© 2003 prentice-hall, inc.chap 13-1 business statistics: a first course (3 rd edition) chapter 13...

© 2003 Prentice-Hall, Inc. Chap 13-1

Business Statistics: A First Course

(3rd Edition)

Chapter 13Statistical Applications in Quality and Productivity

Management


Chapter Topics

Total Quality Management (TQM) Theory of Management (Deming’s

Fourteen Points) The Theory of Control Charts

Common-cause variation versus special-cause variation

Control Charts for the Proportion of Nonconforming Items


Chapter Topics

Process Variability Control Charts for the Mean and the

Range

(continued)


Themes of Quality Management

1. Primary Focus on Process Improvement2. Most Variation in Process due to System3. Teamwork is Integral to Quality

Management4. Customer Satisfaction is a Primary Goal5. Organization Transformation Necessary6. Remove Fear7. Higher Quality Costs Less


Deming’s 14 Points: Point 1:

Plan

DoStudy

Act

Point 1. Create Constancy of Purpose

The Shewhart-Deming CycleFocuses on Constant Improvement


Deming’s 14 Points: Points 2 and 3

Point 2. Adopt New Philosophy

Better to be proactive and change before crisis occurs.

Point 3. Cease Dependence on Mass Inspection to Achieve Quality

Any inspection whose purpose is to improve quality is too late.


Point 4. End the Practice of Awarding Business on the Basis of Price Tag Alone

Develop long term relationship between purchaser and supplier.

Point 5. Improve Constantly and Forever

Reinforce the importance of the Shewhart-Deming cycle.




Point 6. Institute Training

Especially important for managers to understand the difference between special causes and common causes.

Point 7. Adopt and Institute Leadership

Differentiate between leadership and supervision. Leadership is to improve the system and achieve greater consistency of performance.


Points 8-12.

Drive out Fear

Break Down Barriers Between Staff Areas

Eliminate Slogans

Eliminate Numerical Quotas for Workforce and Numerical Goals for Management

Remove Barriers to Pride of Workmanship

Deming’s 14 Points: Points 8 to 12

300


Point 13. Encourage Education and Self-Improvement for Everyone

Improved knowledge of people will improve assets of organization.

Point 14. Take Action to Accomplish Transformation

Continually strive toward improvement.


Quality is important


Control Charts

Monitors Variation in Data Exhibits trend - make correction before

process is out of control A Process -- A Repeatable Series of

Steps Leading to A Specific Goal


Control Charts

Show when Changes in Data are Due to: Special or assignable causes

Fluctuations not inherent to a process Represents problems to be corrected Data outside control limits or trend

Chance or common causes Inherent random variations Consist of numerous small causes of random

variability

(continued)


Graph of sample data plotted over time

Process Control Chart

020406080

1 3 5 7 9 11

X

Time

Special Cause Variation

Common Cause Variation

Process Average

Mean

UCL

LCL


Control Limits

UCL = Process Average + 3 Standard Deviations

LCL = Process Average - 3 Standard Deviations

Process Average

UCL

LCL

X

+ 3

- 3

TIME


Types of Error

First Type: Belief that observed value represents special

cause when in fact it is due to common cause

Second Type: Treating special cause variation as if it is

common cause variation


Comparing Control Chart Patterns

X XX

Common Cause Variation: No Points

Outside Control Limits

Special Cause Variation: 2 Points

Outside Control Limits

Downward Pattern: No Points Outside Control Limits but

Trend Exists


When to Take Corrective Action

Corrective Action should be Taken when Observing Points Outside the Control Limits or when a Trend has been Detected Eight consecutive points above the center

line (or eight below) Eight consecutive points that are increasing

(or decreasing)


Out-of-control Processes

If the Control Chart Indicates an Out-of-Control Condition (a Point Outside the Control Limits or Exhibiting Trend), then Both common causes of variation and

assignable causes of variation exist The assignable causes of variation must be

identified If detrimental to the quality, assignable

causes of variation must be removed If increases quality, assignable causes must

be incorporated into the process design


In-control Process

If the Control Chart is not Indicating Any Out-of-Control Condition, then Only common causes of variation exists It is sometimes said to be in a state of

statistical control If the common-cause variation is small, then

control chart can be used to monitor the process

If the common-cause variation is too large, the process needs to be altered


p Chart Control Chart for Proportions

Is an attribute chartattribute chart Shows Proportion of Nonconforming

(success success ) Items e.g., Count # of nonconforming chairs &

divide by total chairs inspected

Chair is either conforming or nonconforming Used with Equal or Unequal Sample Sizes

Over Time Unequal sizes should not differ by more than

±25% from average sample size


p Chart Control Limits

(1 )max 0, 3p

p pLCL p

n

(1 )3p

p pUCL p

n

1

k

ii

nn

k

Average Group Size

1

1

k

iik

ii

Xp

n

Average Proportion of Nonconforming Items

# Defective Items in Sample i

Size of Sample i

# of Samples


p Chart Example

You’re manager of a 500-room hotel. You want to achieve the highest level of service. For 7 days, you collect data on the readiness of 200 rooms. Is the process in control?


p Chart Hotel Data

# NotDay # Rooms Ready Proportion

1 200 16 0.0802 200 7 0.0353 200 21 0.1054 200 17 0.0855 200 25 0.1256 200 19 0.0957 200 16 0.080


1

1

121.0864

1400

k

iik

ii

Xp

n

p Chart Control Limits Solution

16 + 7 +...+ 16

1 1400200

7

k

ii

nn

k

1 .0864 1 .08643 .0864 3

200

.0864 .0596 or .0268,.1460

p pp

n


Mean

p Chart Control Chart Solution

UCL

LCL

0.00

0.05

0.10

0.15

1 2 3 4 5 6 7

P

Day

Individual points are distributed around without any pattern. Any improvement in the process must come from reduction of common-cause variation, which is the responsibility of the management.

p

p


p Chart in PHStat

PHStat | Control Charts | p Chart …

Excel Spreadsheet for the Hotel Room Example

Microsoft Excel Worksheet


Worker Day 1 Day 2 Day 3 All Days

A 9 (18%) 11 (12%) 6 (12%) 26 (17.33%)

B 12 (24%) 12 (24%) 8 (16%) 32 (21.33%)

C 13 (26%) 6 (12%) 12 (24%) 31(20.67%)

D 7 (14%) 9 (18%) 8 (16%) 24 (16.0%)

Totals 41 38 34 113

Understanding Process Variability:

Red Bead Example

Four Workers (A, B, C, D) spent 3 days to collect beads, at 50 beads per day. The expected number of red beads to be collected per day per worker is 10 or 20%.


Average Day 1 Day 2 Day 3 All Days

X 10.25 9.5 8.5 9.42

p 20.5% 19% 17% 18.83%


Example Calculations

113.1883

50(12)p

(1 ) .1883(1 .1883)3 .1883 3

50 .1883 .1659

p pp

n

_

.1883 .1659 .0224

.1883 +.1659 .3542

LCL

UCL


0 A1 B1 C1 D1 A2 B2 C2 D2 A3 B3 C3 D3


Example Control Chart

.30

.20

.10

p

UCL

LCL

_


Morals of the Example

1. Variation is an inherent part of any process.

2. The system is primarily responsible for worker performance.

3. Only management can change the system.

4. Some workers will always be above average,

and some will be below.


Variables Control Charts: R Chart

Monitors Variability in Process Characteristic of interest is measured on

numerical scale Is a variables control chartvariables control chart

Shows Sample Range Over Time Difference between smallest & largest

values in inspection sample e.g., Amount of time required for luggage to

be delivered to hotel room


R Chart Control Limits

Sample Range at Time i or subgroup i

# Samples

From Table E.94RUCL D R

3RLCL D R

1

k

ii

RR

k


R Chart Example

You’re manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on 5 deliveries per day. Is the process in control?


R Chart and Mean Chart Hotel Data

Sample SampleDay Average Range

1 5.32 3.852 6.59 4.273 4.88 3.284 5.70 2.995 4.07 3.616 7.34 5.047 6.79 4.22


R Chart Control Limits Solution

From Table E.9 (n = 5)

1 3.85 4.27 4.223.894

7

k

ii

RR

k

4

3

2.114 3.894 8.232

0 3.894 0

R

R

UCL D R

LCL D R


R Chart Control Chart Solution

UCL

02468

1 2 3 4 5 6 7

Minutes

Day

LCL

R_


Variables Control Charts: Mean Chart (The Chart)

Shows Sample Means Over Time Compute mean of inspection sample over

time e.g., Average luggage delivery time in hotel

Monitors Process Average Must be preceded by examination of the R

chart to make sure that the process is in-control

X


Mean Chart

Sample Range at Time i

# Samples

Sample Mean at Time i

Computed From Table E.9

2XUCL X A R

2XLCL X A R

1 1 and

k k

i ii i

X RX R

k k


Mean Chart Example

You’re manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on 5 deliveries per day. Is the process in control?


R Chart and Mean Chart Hotel Data

Sample SampleDay Average Range

1 5.32 3.852 6.59 4.273 4.88 3.284 5.70 2.995 4.07 3.616 7.34 5.047 6.79 4.22


Mean Chart Control Limits Solution

1

1

2

2

5.32 6.59 6.795.813

7

3.85 4.27 4.223.894

7

5.813 0.577 3.894 8.060

5.813 0.577 3.894 3.566

k

i

i

k

ii

X

X

XX

k

RR

k

UCL X A R

LCL X A R

From Table E.9 (n = 5)


Mean Chart Control Chart Solution

UCL

LCL

02468

1 2 3 4 5 6 7

Minutes

Day

X__


R Chart and Mean Chart in PHStat

PHStat | Control Charts | R & Xbar Charts …

Excel Spreadsheet for The Hotel Room Example

Microsoft Excel Worksheet


Chapter Summary

Described Total Quality Management (TQM)

Addressed the Theory of Management Deming’s fourteen points

Discussed the Theory of Control Charts Common-cause variation versus special-

cause variation


Chapter Summary

Computed Control Charts for the Proportion of Nonconforming Items

Described Process Variability Computed Control Charts for the Mean

and the Range

(continued)

© 2003 prentice-hall, inc.chap 13-1 business statistics: a first course (3 rd edition) chapter 13...

Documents

quality management4

special causes

controla process

process improvement2

common causesecond type

numerical quotas

numerical goals

standard deviationslcl