Transcript Basic Business Statistics (9th Edition)

Basic Business Statistics
(9th Edition)
Chapter 18
Statistical Applications in Quality
and Productivity Management
© 2004 Prentice-Hall, Inc.
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
© 2004 Prentice-Hall, Inc.
Chap 18-4
Deming’s 14 Points:
Point 1:
Point 1. Create Constancy of Purpose
Act
Plan
Study
Do
The Shewhart-Deming Cycle
Focuses on Constant Improvement
© 2004 Prentice-Hall, Inc.
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.
© 2004 Prentice-Hall, Inc.
Chap 18-7
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.
© 2004 Prentice-Hall, Inc.
Chap 18-8
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
© 2004 Prentice-Hall, Inc.
Chap 18-9
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 the assets of
the organization.
Point 14. Take Action to Accomplish Transformation
Continually strive toward improvement.
© 2004 Prentice-Hall, Inc.
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
© 2004 Prentice-Hall, Inc.
Chap 18-12
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


© 2004 Prentice-Hall, Inc.
Inherent random variations
Consist of numerous small causes of random
variability
Chap 18-14
Process Control Chart
Graph of sample data plotted over time
Special
Cause
Variation
Common
Cause
Variation
© 2004 Prentice-Hall, Inc.
80
60
40
20
0
X
UCL
Mean
LCL
Process
Average

1 2 3 4 5 6 7 8 9 101112
Time
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
Comparing Control Chart
Patterns
X
X
Common Cause
Variation: No Points
Outside Control
Limits
© 2004 Prentice-Hall, Inc.
X
Special Cause
Variation: 2 Points
Outside Control
Limits
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)
© 2004 Prentice-Hall, Inc.
Chap 18-19
Out-of-Control Processes

If the Control Chart Indicates an Out-ofControl 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


© 2004 Prentice-Hall, Inc.
If detrimental to quality, assignable causes of
variation must be removed
If increases quality, assignable causes must be
incorporated into the process design
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


© 2004 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 18-21
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
© 2004 Prentice-Hall, Inc.
Chap 18-22
p Chart
Control Limits
LC L p  p  3
p (1  p )
n
Average Group Size
k
n 
n
i
# of Samples

k
n
i 1
© 2004 Prentice-Hall, Inc.
n
Average Proportion of
Nonconforming Items
k
# Defective
Items in
Xi
Sample i
i 1
p 
i 1
k
UCLp  p  3
p (1  p )
i
Size of
Sample i
Chap 18-23
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?
© 2004 Prentice-Hall, Inc.
Chap 18-24
p Chart
Hotel Data
Day
1
2
3
4
5
6
7
© 2004 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 18-25
p Chart
Control Limits Solution
n
n
i 1
16 + 7 +...+ 16
k
k
i

1400
k
 200
p
7
X
i
i 1
k
n

121
 .0864
1400
i
i 1
p3

p 1 p

 .0864  3
.0864  1  .0864 
n
200
 .0864  .0596 or  .0268, .1460 
© 2004 Prentice-Hall, Inc.
Chap 18-26
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.
© 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
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
© 2004 Prentice-Hall, Inc.
41
38
34
All Days
113
Chap 18-29
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%
_
p
113
 .1883
p3
50(12)
p (1  p )
 .1883  3
All Days
.1883(1  .1883)
n
50
 .1883  .1659
L C L  .1 8 8 3  .1 6 5 9  .0 2 2 4
U C L  .1 8 8 3 +.1 6 5 9  .3 5 4 2
© 2004 Prentice-Hall, Inc.
Chap 18-30
Understanding Process Variability:
Example Control Chart
UCL
.30
_
p
.20
.10
LCL
0
A1
© 2004 Prentice-Hall, Inc.
B1
C1
D1
A2
B2 C2
D2
A3
B3
C3
D3
Chap 18-31
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)


Shows Total Number of Nonconforming Items
in a Unit


Is an attribute chart
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
L C Lc  c  3 c
U C Lc  c  3 c
Average Number of
Occurrences
k
c 
c
i
# of Occurrences in Sample i
i 1
k
# 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
c Chart: Hotel Data
Day
1
2
3
4
5
6
7
© 2004 Prentice-Hall, Inc.
# Rooms
200
200
200
200
200
200
200
# Not
Ready
16
7
21
17
25
19
16
Chap 18-36
c Chart:
Control Limits Solution
k
c 
c
i 1
k
i

16  7 
 19  16
 17.286
7
L C L c  c  3 c  17.286  3 17.285  4.813
U C L c  c  3 c  29.759
© 2004 Prentice-Hall, Inc.
Chap 18-37
c Chart:
Control Chart Solution
30
c
UCL
20
c
10
LCL
0
1
2
3
4
Day
5
6
7
Individual points are distributed around c without any pattern.
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 18-38
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
© 2004 Prentice-Hall, Inc.
Chap 18-39
R Chart
Control Limits
UC L R  D 4 R
From
Table
L C LR  D3 R
k
R 
R
i 1
k
© 2004 Prentice-Hall, Inc.
i
Sample Range at
Time i or Sample i
# Samples
Chap 18-40
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?
© 2004 Prentice-Hall, Inc.
Chap 18-41
R Chart and Mean Chart
Hotel Data
Day
1
2
3
4
5
6
7
© 2004 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 18-42
R Chart
Control Limits Solution
k
R 
R
i 1
k
i

3.85  4.27 
 4.22
 3.894
7
U C L R  D 4  R  2.114  3.894  8.232
L C L R  D 3  R  0  3.894  0
© 2004 Prentice-Hall, Inc.
From Table
(n = 5)
Chap 18-43
R Chart
Control Chart Solution
Minutes
8
6
4
2
0
1
2
© 2004 Prentice-Hall, Inc.
UCL
_
R
LCL
3
4
Day
5
6
7
Chap 18-44
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
© 2004 Prentice-Hall, Inc.
Chap 18-45
Mean Chart
Computed
From
Table
Sample
Mean at
Time i
UC L X  X  A2 R
LC L X  X  A2 R
k
X 

i 1
k
© 2004 Prentice-Hall, Inc.
k
Xi
and
R 
R
i 1
k
i
Sample
Range
at Time i
# Samples
Chap 18-46
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
R Chart and Mean Chart
Hotel Data
Day
1
2
3
4
5
6
7
© 2004 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 18-48
Mean Chart
Control Limits Solution
k
X 

X
i
i 1

5 .3 2  6 .5 9 
k
7
k
R 

i 1
k
Ri

3 .8 5  4 .2 7 
 6 .7 9
 5 .8 1 3
From
Table E.9
(n = 5)
 4 .2 2
 3 .8 9 4
7
U C L X  X  A 2  R  5 .8 1 3  0 .5 7 7  3 .8 9 4  8 .0 6 0
L C L X  X  A 2  R  5 .8 1 3  0 .5 7 7  3 .8 9 4  3 .5 6 6
© 2004 Prentice-Hall, Inc.
Chap 18-49
Mean Chart
Control Chart Solution
Minutes
8
6
4
2
0
1
2
© 2004 Prentice-Hall, Inc.
UCL
__
X
LCL
3
4
Day
5
6
7
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 X and Standard Deviation
Estimated by R / d 2
© 2004 Prentice-Hall, Inc.
Chap 18-53
Estimating Process Capability
(continued)

For a Characteristic with an LSL and a USL
P (an o u tco m e w ill b e w ith in sp ecificatio n )

 P (L S L  X  U S L )
 LSL  X
U SL  X
= P
 Z 
 R/d
R / d2
2






where Z is a standardized normal random variable
© 2004 Prentice-Hall, Inc.
Chap 18-54
Estimating Process Capability
(continued)

For a Characteristic with Only a LSL
P (an o u tco m e w ill b e w ith in sp ecificatio n )

 P (L S L  X )
 LSL  X

= P
 Z
 R/d

2



where Z is a standardized normal random variable
© 2004 Prentice-Hall, Inc.
Chap 18-55
Estimating Process Capability
(continued)

For a Characteristic with Only a USL
P (an o u tco m e w ill b e w ith in sp ecificatio n )

 P (X  U S L )

U SL  X
= PZ 

R / d2






where Z is a standardized normal random variable
© 2004 Prentice-Hall, Inc.
Chap 18-56
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
Process Capability:
Hotel Data
Day
1
2
3
4
5
6
7
© 2004 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 18-58
Process Capability:
Hotel Example Solution
n 5
X  5.813
R  3 .8 9 4
an d d 2  2 .3 2 6
P (A delivery is m ade w ithin specificatio n )
= P ( X  10)
10  5.813 

= PZ 

3.894 / 2.326 

= P ( Z  2.50)  .9938
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.
© 2004 Prentice-Hall, Inc.
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


Cp 
U SL  LSL
6  R / d2 

specification spread
process spread
Cp>1 implies that a process has the potential of
having more than 99.73% of outcomes within
specifications
© 2004 Prentice-Hall, Inc.
Chap 18-60
Capability Indices

(continued)
Measures of Actual Process Performance

For one-sided specification limits



© 2004 Prentice-Hall, Inc.
CPL 
CPU 
X  L SL
3 R / d2 
U SL  X
3 R / d2 
CPL (CPU) >1 implies that the process mean is
more than 3 standard deviations away from the
lower (upper) specification limit
Chap 18-61
Capability Indices

(continued)
For two-sided specification limits



© 2004 Prentice-Hall, Inc.
C p k  m in  C P L , C P U 
Cpk = 1 indicates that the process average is 3
standard deviations away from the closest
specification limit
Larger Cpk indicates larger capability of meeting the
requirements
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
Process Capability:
Hotel Data
Day
1
2
3
4
5
6
7
© 2004 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 18-64
Process Capability:
Hotel Example Solution
n 5
CPU 
X  5.813
U SL  X
3 R / d2 

R  3 .8 9 4
10  5.813
3  3.894 / 2.326 
an d d 2  2 .3 2 6
 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
© 2004 Prentice-Hall, Inc.
Chap 18-66
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
© 2004 Prentice-Hall, Inc.
Chap 18-67