Business Statistics:
A First Course
(3rd Edition)
Chapter 13
Statistical Applications in Quality
and Productivity Management
© 2003 Prentice-Hall, Inc.
Chap 13-1
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
© 2003 Prentice-Hall, Inc.
Chap 13-2
Chapter Topics
(continued)

Process Variability

Control Charts for the Mean and the Range
© 2003 Prentice-Hall, Inc.
Chap 13-3
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. Organization Transformation Necessary
6. Remove Fear
7. Higher Quality Costs Less
© 2003 Prentice-Hall, Inc.
Chap 13-4
Deming’s 14 Points:
Point 1:
Point 1. Create Constancy of Purpose
Act
Plan
Study
Do
The Shewhart-Deming Cycle
Focuses on Constant Improvement
© 2003 Prentice-Hall, Inc.
Chap 13-5
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.
© 2003 Prentice-Hall, Inc.
Chap 13-6
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.
© 2003 Prentice-Hall, Inc.
Chap 13-7
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.
© 2003 Prentice-Hall, Inc.
Chap 13-8
Deming’s 14 Points:
Points 8 to 12
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
© 2003 Prentice-Hall, Inc.
300
Chap 13-9
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 assets of
organization.
Point 14. Take Action to Accomplish Transformation
Continually strive toward improvement.
© 2003 Prentice-Hall, Inc.
Chap 13-10
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
© 2003 Prentice-Hall, Inc.
Chap 13-11
Control Charts

(continued)
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


© 2003 Prentice-Hall, Inc.
Inherent random variations
Consist of numerous small causes of random
variability
Chap 13-12
Process Control Chart
Graph of sample data plotted over time
© 2003 Prentice-Hall, Inc.
X
UCL
Mean
Process
Average

11
Time
9
7
5
LCL
3
Common
Cause
Variation
80
60
40
20
0
1
Special
Cause
Variation
Chap 13-13
Control Limits
UCL = Process Average + 3 Standard Deviations
LCL = Process Average - 3 Standard Deviations
X
UCL
+ 3
Process
Average
- 3
LCL
TIME
© 2003 Prentice-Hall, Inc.
Chap 13-14
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
© 2003 Prentice-Hall, Inc.
Chap 13-15
Comparing Control Chart
Patterns
X
X
Common Cause
Variation: No Points
Outside Control
Limits
© 2003 Prentice-Hall, Inc.
X
Special Cause
Variation: 2 Points
Outside Control
Limits
Downward Pattern:
No Points Outside
Control Limits but
Trend Exists
Chap 13-16
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)
© 2003 Prentice-Hall, Inc.
Chap 13-17
Out-of-control Processes

If the Control Chart Indicates an Out-ofControl 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


© 2003 Prentice-Hall, Inc.
If detrimental to the quality, assignable causes of
variation must be removed
If increases quality, assignable causes must be
incorporated into the process design
Chap 13-18
In-control Process

If the Control Chart is not Indicating Any Outof-Control Condition, then


Only common causes of variation exists
It is sometimes said to be in a state of statistical
control


© 2003 Prentice-Hall, Inc.
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 13-19
p Chart

Control Chart for Proportions


Is an attribute chart
Shows Proportion of Nonconforming (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

© 2003 Prentice-Hall, Inc.
Unequal sizes should not differ by more than ±25%
from average sample size
Chap 13-20
p Chart
Control Limits

p(1  p)
p (1  p ) 
LCLp  max  0, p  3
 UCLp  p  3
n 
n

Average Group Size
k
n
n
i 1
k
i
Average Proportion of
Nonconforming Items
k
# Defective
Items in
Xi
Sample i
i 1
p
# of Samples

k
n
i 1
© 2003 Prentice-Hall, Inc.
i
Size of
Sample i
Chap 13-21
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?
© 2003 Prentice-Hall, Inc.
Chap 13-22
p Chart
Hotel Data
Day
1
2
3
4
5
6
7
© 2003 Prentice-Hall, Inc.
# Rooms
200
200
200
200
200
200
200
# Not
Ready
16
7
21
17
25
19
16
Proportion
0.080
0.035
0.105
0.085
0.125
0.095
0.080
Chap 13-23
p Chart
Control Limits Solution
n
n
i 1
k
i
16 + 7 +...+ 16
k
k
1400

 200
7
p
X
i 1
k
n
i 1

i
121

 .0864
1400
i
  .0864  3
.0864 1  .0864 
p3
200
n
 .0864  .0596 or .0268,.1460 
p 1 p
© 2003 Prentice-Hall, Inc.
Chap 13-24
p Chart
Control Chart Solution
0.15
P
UCL
0.10
Mean p
0.05
LCL
0.00
1
2
3
4
Day
5
6
7
Individual points are distributed around p without any pattern.
Any improvement in the process must come from reduction of
common-cause variation, which is the responsibility of the
management.
© 2003 Prentice-Hall, Inc.
Chap 13-25
p Chart in PHStat


PHStat | Control Charts | p Chart …
Excel Spreadsheet for the Hotel Room
Example
© 2003 Prentice-Hall, Inc.
Chap 13-26
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%.
Worker
Day 1
Day 2
Day 3
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
© 2003 Prentice-Hall, Inc.
41
38
34
All Days
113
Chap 13-27
Understanding Process Variability:
Example Calculations
Average
Day 1
Day 2
Day 3
X
10.25
9.5
8.5
9.42
p
20.5%
19%
17%
18.83%
_
113
p
 .1883
50(12)
All Days
p(1  p)
.1883(1  .1883)
p 3
 .1883  3
n
50
 .1883  .1659
LCL  .1883  .1659  .0224
UCL  .1883 +.1659  .3542
© 2003 Prentice-Hall, Inc.
Chap 13-28
Understanding Process Variability:
Example Control Chart
UCL
.30
_
p
.20
.10
LCL
0
A1
© 2003 Prentice-Hall, Inc.
B1
C1
D1
A2
B2 C2
D2
A3
B3
C3
D3
Chap 13-29
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.
© 2003 Prentice-Hall, Inc.
Chap 13-30
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
© 2003 Prentice-Hall, Inc.
Chap 13-31
R Chart
Control Limits
UCLR  D4 R
From
Table E.9
LCLR  D3 R
k
R
© 2003 Prentice-Hall, Inc.
R
i 1
k
i
Sample Range at
Time i or
subgroup i
# Samples
Chap 13-32
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?
© 2003 Prentice-Hall, Inc.
Chap 13-33
R Chart and Mean Chart
Hotel Data
Day
1
2
3
4
5
6
7
© 2003 Prentice-Hall, Inc.
Sample
Average
5.32
6.59
4.88
5.70
4.07
7.34
6.79
Sample
Range
3.85
4.27
3.28
2.99
3.61
5.04
4.22
Chap 13-34
R Chart
Control Limits Solution
k
R
R
i 1
k
i
3.85  4.27 

7
 4.22
 3.894
UCLR  D4  R  2.114  3.894  8.232
LCLR  D3  R  0  3.894  0
© 2003 Prentice-Hall, Inc.
From Table
E.9 (n = 5)
Chap 13-35
R Chart
Control Chart Solution
Minutes
8
6
4
2
0
1
2
© 2003 Prentice-Hall, Inc.
UCL
_
R
LCL
3
4
Day
5
6
7
Chap 13-36
Variables Control Charts: Mean
Chart (The X 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
© 2003 Prentice-Hall, Inc.
Chap 13-37
Mean Chart
UCLX  X  A2 R
LCLX  X  A2 R
k
X
© 2003 Prentice-Hall, Inc.
X
i 1
k
Computed
From
Table E.9
Sample
Mean at
Time i
k
i
and R 
R
i 1
k
i
Sample
Range
at Time i
# Samples
Chap 13-38
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?
© 2003 Prentice-Hall, Inc.
Chap 13-39
R Chart and Mean Chart
Hotel Data
Day
1
2
3
4
5
6
7
© 2003 Prentice-Hall, Inc.
Sample
Average
5.32
6.59
4.88
5.70
4.07
7.34
6.79
Sample
Range
3.85
4.27
3.28
2.99
3.61
5.04
4.22
Chap 13-40
Mean Chart
Control Limits Solution
k
X 
X
i 1
k
i
5.32  6.59 

7
 6.79
 5.813
k
R
R
i 1
k
i
3.85  4.27 

7
 4.22
 3.894
From
Table E.9
(n = 5)
UCLX  X  A2  R  5.813  0.577  3.894  8.060
LCLX  X  A2  R  5.813  0.577  3.894  3.566
© 2003 Prentice-Hall, Inc.
Chap 13-41
Mean Chart
Control Chart Solution
Minutes
8
6
4
2
0
1
2
© 2003 Prentice-Hall, Inc.
UCL
__
X
LCL
3
4
Day
5
6
7
Chap 13-42
R Chart and Mean Chart in
PHStat


PHStat | Control Charts | R & Xbar Charts …
Excel Spreadsheet for The Hotel Room
Example
© 2003 Prentice-Hall, Inc.
Chap 13-43
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
© 2003 Prentice-Hall, Inc.
Chap 13-44
Chapter Summary



(continued)
Computed Control Charts for the Proportion of
Nonconforming Items
Described Process Variability
Computed Control Charts for the Mean and
the Range
© 2003 Prentice-Hall, Inc.
Chap 13-45