© 2004 Prentice-Hall, Inc.
(9 th Edition)
Chap 18-1

Chapter Topics





Total Quality Management (TQM)
Theory of Management (Deming’s Fourteen
Points)
Six Sigma ® Management Approach
The Theory of Control Charts

Common-cause variation versus special-cause variation
Control Charts for the Proportion of
Nonconforming Items
© 2004 Prentice-Hall, Inc. Chap 18-2

Chapter Topics
(continued)




Process Variability
The c Chart
Control Charts for the Mean and the Range
Process Capability
© 2004 Prentice-Hall, Inc. Chap 18-3

Themes of Quality Management
1. Primary Focus on Process Improvement
2. Most Variation in Process Due to System
3. Teamwork is Integral to Quality Management
4. Customer Satisfaction is a Primary Goal
5. Organizational Transformation Necessary
6. Remove Fear
7. Higher Quality Costs Less
Chap 18-4 © 2004 Prentice-Hall, Inc.

Deming’s 14 Points:
Point 1:
Act
Plan
Study
Do
© 2004 Prentice-Hall, Inc.
The Shewhart-Deming Cycle
Focuses on Constant Improvement
Chap 18-5

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.
© 2004 Prentice-Hall, Inc. Chap 18-6

Deming’s 14 Points:
Points 4 and 5
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.
Chap 18-7 © 2004 Prentice-Hall, Inc.

Deming’s 14 Points:
Points 6 and 7
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.
Chap 18-8 © 2004 Prentice-Hall, Inc.

Deming’s 14 Points:
Points 8 to 12
8. Drive Out Fear
9. Break Down Barriers between Staff Areas
10. Eliminate Slogans
11. Eliminate Numerical Quotas for Workforce and Numerical Goals for Management
12. Remove Barriers to Pride of
Workmanship
300
Chap 18-9 © 2004 Prentice-Hall, Inc.

Deming’s 14 Points:
Points 13 and 14
Point 13. Encourage Education and Self-Improvement for Everyone
Quality is important
Improved knowledge of people will improve the assets of the organization.
Point 14. Take Action to Accomplish Transformation
© 2004 Prentice-Hall, Inc.
Continually strive toward improvement.
Chap 18-10

Six Sigma ® Management


A Managerial Approach Designed to Create
Processes that Result in No More Than 3.4
Defects Per Million
A Method for Breaking Processes into a Series of Steps in Order to Eliminate Defects and
Produce Near Perfect Results

(1) Define: Define the problem along with costs, benefits and the impact on customers

(2) Measure: Develop operational definitions for each Critical-to-Quality characteristic and verify measurement procedure to achieve consistency over repeated measurements
© 2004 Prentice-Hall, Inc. Chap 18-11

Six Sigma ® Management
(continued)



(3) Analyze: Use control charts to monitor defects and determine the root causes of defects
(4) Improve: Study the importance of each process variable on the Critical-to-Quality characteristic to determine and maintain the best level for each variable in the long term
(5) Control: Avoid potential problems that occur when a process is changed and maintain the gains that have been made in the long term
Chap 18-12 © 2004 Prentice-Hall, Inc.

Control Charts


Monitor Variation in Data

Exhibit trend - make correction before process is out of control
A Process - A Repeatable Series of Steps
Leading to a Specific Goal
© 2004 Prentice-Hall, Inc. Chap 18-13

Control Charts
(continued)

Show When Changes in Data are Due to:


Special or assignable causes



Fluctuations not inherent to a process
Represent 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
Chap 18-14 © 2004 Prentice-Hall, Inc.

Process Control Chart
Graph of sample data plotted over time
Special
Cause
Variation
80
60
40
Common
20
0
X
Cause
1 2 3 4 5 6 7 8 9 101112
Time
Variation
UCL
LCL
Mean
Process
Average

© 2004 Prentice-Hall, Inc. Chap 18-15

Control Limits
UCL = Process Average + 3 Standard Deviations
LCL = Process Average - 3 Standard Deviations
X
UCL
+ 3

Process
Average
- 3

LCL
TIME
© 2004 Prentice-Hall, Inc. Chap 18-16

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
© 2004 Prentice-Hall, Inc. Chap 18-17

X
Comparing Control Chart
Patterns
X X
Common Cause
Variation: No Points
Outside Control
Limits
Special Cause
Variation: 2 Points
Outside Control
Limits
© 2004 Prentice-Hall, Inc.
Downward Pattern:
No Points Outside
Control Limits but
Trend Exists
Chap 18-18

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
(decreasing)
Chap 18-19 © 2004 Prentice-Hall, Inc.

Out-of-Control Processes

If the Control Chart Indicates an Out-of-
Control Condition (a Point Outside the Control
Limits or Exhibiting Trend)


Contains both common causes of variation and assignable causes of variation
The assignable causes of variation must be identified


If detrimental to quality, assignable causes of variation must be removed
If increases quality, assignable causes must be incorporated into the process design
© 2004 Prentice-Hall, Inc. Chap 18-20

In-Control Process

If the Control Chart is Not Indicating Any Outof-Control Condition, then

Only common causes of variation exist

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
Chap 18-21 © 2004 Prentice-Hall, Inc.

p Chart



Control Chart for Proportions

Is an attribute chart
Shows Proportion of Nonconforming 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
Chap 18-22 © 2004 Prentice-Hall, Inc.

p Chart
Control Limits
LCL p
 
3 p (1
 p ) n
UCL p
 
3 p (1
 p ) n
Average Group Size n
 i k 

1 n i k
# of Samples
© 2004 Prentice-Hall, Inc. p
Average Proportion of
Nonconforming Items
 i k 

1
X i i k 

1 n i
# Defective
Items in
Sample i
Size of
Sample i
Chap 18-23

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?
© 2004 Prentice-Hall, Inc. p Chart
Example
Chap 18-24

© 2004 Prentice-Hall, Inc. p Chart
Hotel Data
# Not
Day # Rooms Ready Proportion
5
6
7
3
4
1
2
200
200
200
200
200
200
200
16
7
21
17
25
19
16
0.080
0.035
0.105
0.085
0.125
0.095
0.080
Chap 18-25

n
 i k 

1 n i k
 p

3 p
 
 n

© 2004 Prentice-Hall, Inc. p Chart
Control Limits Solution

1400
7

200
16 + 7 +...+ 16 p
 i k 

1
X i i k 

1 n i

121
1400

.0864


200

Chap 18-26

p Chart
Control Chart Solution
0.15
P
0.10
0.05
0.00
UCL
LCL
1 2 3 4 5 6 7
Day
Mean p p
Any improvement in the process must come from reduction of common-cause variation, which is the responsibility of the management.
© 2004 Prentice-Hall, Inc. Chap 18-27

p Chart in PHStat

PHStat | Control Charts | p Chart …

Excel Spreadsheet for the Hotel Room
Example
© 2004 Prentice-Hall, Inc. Chap 18-28

Understanding Process Variability:
Red Bead Example
Four workers (A, B, C, D) spend 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%.
Worker
A
B
C
Day 1
9 (18%)
12 (24%)
13 (26%)
D 7 (14%)
Totals
© 2004 Prentice-Hall, Inc.
41
Day 2 Day 3 All Days
11 (12%) 6 (12%) 26 (17.33%)
12 (24%) 8 (16%) 32 (21.33%)
6 (12%) 12 (24%) 31(20.67%)
9 (18%) 8 (16%) 24 (16.0%)
38 34 113
Chap 18-29

Understanding Process Variability:
Example Calculations
Average Day 1
_
X 10.25
p 20.5%
Day 2
9.5
19% p

113
50(12)

.1883
p

3 p (1
 p )
 n
LCL

.1883 .1659

.0224
UCL

.1883 +.1659

.3542
© 2004 Prentice-Hall, Inc.
Day 3
8.5
17%
All Days
9.42
18.83%
50
Chap 18-30

Understanding Process Variability:
Example Control Chart
UCL
.30
.20
.10
0 A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
A
3
B
3
LCL
C
3
D
3
_ p
Chap 18-31 © 2004 Prentice-Hall, Inc.

Morals of the Example

Variation is an inherent part of any process.

The system is primarily responsible for worker performance.

Only management can change the system.

Some workers will always be above average, and some will be below.
© 2004 Prentice-Hall, Inc. Chap 18-32

The c Chart



Control Chart for Number of Nonconformities
(Occurrences) in a Unit (an Area of
Opportunity)

Is an attribute chart
Shows Total Number of Nonconforming Items in a Unit

E.g., Count # of defective chairs manufactured per day
Assume that the Size of Each Subgroup Unit
Remains Constant
© 2004 Prentice-Hall, Inc. Chap 18-33

c Chart Control Limits
LCL c 3 c c
 
UCL c 3 c c
 
Average Number of c
 i


1 c i k
# of Occurrences in Sample i
# of Samples
© 2004 Prentice-Hall, Inc. Chap 18-34

c 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?
© 2004 Prentice-Hall, Inc. Chap 18-35

© 2004 Prentice-Hall, Inc. c Chart: Hotel Data
# Not
Day # Rooms Ready
5
6
7
3
4
1
2
200
200
200
200
200
200
200
16
7
21
17
25
19
16
Chap 18-36

c Chart:
Control Limits Solution i k 

1 c i c
 
16 7 19 16 k
LCL c
 
3 c

7

17.286
17.286 3 17.285

4.813
UCL c
 
3 c

29.759
Chap 18-37 © 2004 Prentice-Hall, Inc.

c Chart:
Control Chart Solution c
30 UCL
20 c
10
LCL
0
1 2 3 4 5 6 7
Day c
Any improvement in the process must come from reduction of common-cause variation, which is the responsibility of the management.
Chap 18-38 © 2004 Prentice-Hall, Inc.

Variables Control Charts:
R Chart


Monitors Variability in Process


Characteristic of interest is measured on numerical scale
Is a variables 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
Chap 18-39 © 2004 Prentice-Hall, Inc.

R Chart
Control Limits
© 2004 Prentice-Hall, Inc.
UCL
R

D R
4
LCL
R

D R
3
R
 i k 

1 k
R i
From
Table
Sample Range at
Time i or Sample i
# Samples
Chap 18-40

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?
© 2004 Prentice-Hall, Inc.
R Chart
Example
Chap 18-41

© 2004 Prentice-Hall, Inc.
R Chart and Mean Chart
Hotel Data
Sample Sample
Day Average Range
5
6
7
3
4
1
2
5.32
6.59
4.88
5.70
4.07
7.34
6.79
3.85
4.27
3.28
2.99
3.61
5.04
4.22
Chap 18-42

R Chart
Control Limits Solution
R
 i k 

1
R i k

3.85 4.27
 
4.22
7

3.894
UCL
R

D R
4
 
2.114 3.894

8.232
LCL
R

D R
3
0 3.894

0
From Table
( n = 5)
Chap 18-43 © 2004 Prentice-Hall, Inc.

R Chart
Control Chart Solution
© 2004 Prentice-Hall, Inc.
6
4
2
0
8
Minutes UCL
LCL
1 2 3 4 5 6 7
Day
_
R
Chap 18-44

Variables Control Charts: Mean
X


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
© 2004 Prentice-Hall, Inc. Chap 18-45

Mean Chart
X
UCL
X

X

A R
2
LCL
X

X

A R
2
 i k 

1
X i k
and R
 i k 

1
Computed
From
Table
Sample
Mean at
Time i
Sample
Range at Time i k
R i
# Samples
Chap 18-46 © 2004 Prentice-Hall, Inc.

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?
© 2004 Prentice-Hall, Inc. Chap 18-47

© 2004 Prentice-Hall, Inc.
R Chart and Mean Chart
Hotel Data
Sample Sample
Day Average Range
5
6
7
3
4
1
2
5.32
6.59
4.88
5.70
4.07
7.34
6.79
3.85
4.27
3.28
2.99
3.61
5.04
4.22
Chap 18-48

Mean Chart
Control Limits Solution
X
R

 i k i k 

1
X i


1 k k
R i


5.32

6.59
 
6.79
7
3.85

4.27
7
 
4.22

5.813
From
Table E.9

3.894
( n = 5)
UCL
X

X

A
2
 
5.813
  
8.060
LCL
X

X

A
2
 
5.813
  
3.566
Chap 18-49 © 2004 Prentice-Hall, Inc.

© 2004 Prentice-Hall, Inc.
Mean Chart
Control Chart Solution
4
2
0
8
Minutes
6
UCL
LCL
1 2 3 4 5 6 7
Day
X
Chap 18-50

R Chart and Mean Chart in PHStat

PHStat | Control Charts | R & Xbar Charts …

Excel Spreadsheet for the Hotel Room
Example
© 2004 Prentice-Hall, Inc. Chap 18-51

Process Capability




Process Capability is the Ability of a Process to
Consistently Meet Specified Customer-Driven
Requirements
Specification Limits are Set by Management in
Response to Customer’s Expectations
The Upper Specification Limit (USL) is the
Largest Value that Can Be Obtained and Still
Conform to Customer’s Expectation
The Lower Specification Limit (LSL) is the
Smallest Value that is Still Conforming
© 2004 Prentice-Hall, Inc. Chap 18-52

Estimating Process Capability

Must Have an In-Control Process First

Estimate the Percentage of Product or Service
Within Specification

Assume the Population of X Values is
Approximately Normally Distributed with Mean
Estimated by
2
Chap 18-53 © 2004 Prentice-Hall, Inc.

Estimating Process Capability
(continued)

For a Characteristic with an LSL and a USL

P(an outcome will be within specification)

P( LSL

X

USL )
= P




LSL

X
2
USL

2
X




 where Z is a standardized normal random variable
Chap 18-54 © 2004 Prentice-Hall, Inc.

Estimating Process Capability
(continued)

For a Characteristic with Only a LSL

P(an outcome will be within specification)

P( LSL

X )
= P




LSL

X
2

Z




 where Z is a standardized normal random variable
Chap 18-55 © 2004 Prentice-Hall, Inc.

Estimating Process Capability
(continued)

For a Characteristic with Only a USL

P(an outcome will be within specification)

P( X

USL )
= P


Z

USL

X


2
 where Z is a standardized normal random variable
Chap 18-56 © 2004 Prentice-Hall, Inc.

Process Capability Example
You’re manager of a 500room hotel. You have instituted a policy that
99% of all luggage deliveries must be completed within 10 minutes or less. For 7 days, you collect data on 5 deliveries per day.
Is the process capable?
© 2004 Prentice-Hall, Inc. Chap 18-57

© 2004 Prentice-Hall, Inc.
Process Capability:
Hotel Data
Sample Sample
Day Average Range
5
6
7
3
4
1
2
5.32
6.59
4.88
5.70
4.07
7.34
6.79
3.85
4.27
3.28
2.99
3.61
5.04
4.22
Chap 18-58

Process Capability:
Hotel Example Solution n

5 X

5.813
R

3.894
and d
2

2.326
P(A delivery is made within specification)
= P( X

10)
= P Z

3.894 / 2.326
= P( Z

2.50)

.9938
© 2004 Prentice-Hall, Inc.
Therefore, we estimate that 99.38% of the luggage deliveries will be made within the 10 minutes or less specification. The process is capable of meeting the 99% goal.
Chap 18-59

Capability Indices


Aggregate Measures of a Process’ Ability to
Meet Specification Limits

The larger (>1) the values, the more capable a process is of meeting requirements
Measure of Process Potential Performance
 C p

USL

LSL
6

/
2

 specification spread process spread

C p
>1 implies that a process has the potential of having more than 99.73% of outcomes within specifications
Chap 18-60 © 2004 Prentice-Hall, Inc.

Capability Indices
(continued)

Measures of Actual Process Performance

For one-sided specification limits

CPL

X

LSL
3

/
2


CPU

USL

X
3

/
2


CPL (CPU)
>1 implies that the process mean is more than 3 standard deviations away from the lower (upper) specification limit
Chap 18-61 © 2004 Prentice-Hall, Inc.

Capability Indices
(continued)

For two-sided specification limits


C
 min

CPL CPU

C pk pk
= 1 indicates that the process average is 3 standard deviations away from the closest specification limit

Larger
C pk indicates larger capability of meeting the requirements
© 2004 Prentice-Hall, Inc. Chap 18-62

Process Capability Example
You’re manager of a 500room hotel. You have instituted a policy that all luggage deliveries must be completed within 10 minutes or less. For 7 days, you collect data on 5 deliveries per day.
Compute an appropriate capability index for the delivery process.
© 2004 Prentice-Hall, Inc. Chap 18-63

© 2004 Prentice-Hall, Inc.
Process Capability:
Hotel Data
Sample Sample
Day Average Range
5
6
7
3
4
1
2
5.32
6.59
4.88
5.70
4.07
7.34
6.79
3.85
4.27
3.28
2.99
3.61
5.04
4.22
Chap 18-64

Process Capability:
Hotel Example Solution n

5 X

5.813
R

3.894
and d
2

2.326
CPU

USL

X
3

/
2


 

0.833672
Since there is only the upper specification limit, we need to only compute
CPU
. The capability index for the luggage delivery process is .8337, which is less than 1. The upper specification limit is less than 3 standard deviations above the mean.
© 2004 Prentice-Hall, Inc. Chap 18-65

Chapter Summary




Described Total Quality Management (TQM)
Addressed the Theory of Management

Deming’s 14 Points
Described the Six Sigma ® Management
Approach
Discussed the Theory of Control Charts

Common-cause variation versus special-cause variation
Chap 18-66 © 2004 Prentice-Hall, Inc.

Chapter Summary
(continued)





Computed Control Charts for the Proportion of
Nonconforming Items
Described Process Variability
Described c Chart
Computed Control Charts for the Mean and the Range
Discussed Process Capability
Chap 18-67 © 2004 Prentice-Hall, Inc.