Chap17 statistical applications on management

Statistics for Managers
Using Microsoft® Excel
4th Edition
Chapter 17
Statistical Applications in Quality and
Productivity Management
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc.

Chap 17-1

Chapter Goals
After completing this chapter, you should be
able to:
 Describe the concepts of Total Quality Management and
Six Sigma® Management

 Explain process variability and the theory of control
charts

 Construct and interpret p charts
 Construct and interpret X and R charts
 Obtain and explain measures of process capability
Statistics for Managers Using
Microsoft Excel, 4e © 2004
Prentice-Hall, Inc.

Chap 17-2

Chapter Overview
Quality Management and
Tools for Improvement
Philosophy of
Quality
Deming’s 14
Points
Six Sigma®
Management
Prentice-Hall, Inc.

Tools for Quality
Improvement
Control
Charts

Process
Capability

p chart
R chart
X chart
Chap 17-3

Total Quality Management


Primary focus is on process improvement



Most variation in a process is due to the
system, not the individual



Teamwork is integral to quality management



Customer satisfaction is a primary goal



Organization transformation is necessary



It is important to remove fear


StatisticsHigher quality costs less
for Managers Using
Prentice-Hall, Inc.

Chap 17-4

Deming’s 14 Points
1. Create a constancy of purpose toward
improvement


become more competitive, stay in business, and provide jobs

2. Adopt the new philosophy


Better to improve now than to react to problems later

3. Stop depending on inspection to achieve
quality -- build in quality from the start


Inspection to find defects at the end of production is too late

4. Stop awarding contracts on the basis of low
bids

Better
Microsoft Excel, to build2004 purchaser/supplier relationships
4e © long-run
Chap 17-5
Prentice-Hall, Inc.


(continued)

5. Improve the system continuously to improve
quality and thus constantly reduce costs
6. Institute training on the job


Workers and managers must know the difference between
common cause and special cause variation

7. Institute leadership


Know the difference between leadership and supervision

8. Drive out fear so that everyone may work
effectively.
9. Break down barriers
Statistics for Managers Using between departments so
that people can work as a team.
Prentice-Hall, Inc.

Chap 17-6

(continued)


10. Eliminate slogans and targets for the
workforce









They can create adversarial relationships

11. Eliminate quotas and management by
numerical goals
12. Remove barriers to pride of workmanship
13. Institute a vigorous program of education
and self-improvement
14. Make the transformation everyone’s job

Prentice-Hall, Inc.

Chap 17-7

The Shewhart-Deming Cycle
Plan

Act

The
Deming
Cycle

Study
Prentice-Hall, Inc.

Do
The key is a
continuous
cycle of
improvement
Chap 17-8

Six Sigma® Management
A method for breaking a process into a series of
steps:
 The goal is to reduce defects and produce near
perfect results
 The Six Sigma® approach allows for a shift of as
much as 1.5 standard deviations, so is
essentially a ±4.5 standard deviation goal
 The mean of a normal distribution ±4.5
standard deviations
Statistics for Managers Using includes all but 3.4 out of a
million
Prentice-Hall, Inc.

Chap 17-9

The Six Sigma® DMAIC Model
DMAIC represents


Define -- define the problem to be solved; list
costs, benefits, and impact to customer



Measure – need consistent measurements for
each Critical-to-Quality characteristic



Analyze – find the root causes of defects



Improve – use experiments to determine
importance of each Critical-to-Quality variable

 Control – maintain
Statistics for Managers Usinggains that have been made
Chap 17-10
Prentice-Hall, Inc.

Theory of Control Charts


A process is a repeatable series of steps
leading to a specific goal



Control Charts are used to monitor variation in
a measured value from a process



Inherent variation refers to process variation
that exists naturally. This variation can be
reduced but not eliminated

Prentice-Hall, Inc.

Chap 17-11

Theory of Control Charts
(continued)


Control charts indicate 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
Chap 17-12
Prentice-Hall, Inc.


Process Variation
Total Process
Common Cause
Special Cause
=
+
Variation
Variation
Variation
Variation is natural; inherent in the world
around us
 No two products or service experiences
are exactly the same
 With a fine enough gauge, all things can
be seen to differ
Chap 17-13
Prentice-Hall, Inc.


Total Process Variation
Total Process
Common Cause
Special Cause
=
+
Variation
Variation
Variation
Variation is often due to differences in:
 People
 Machines
 Materials
 Methods
 Measurement

Microsoft Excel,Environment
4e © 2004
Prentice-Hall, Inc.

Chap 17-14

Common Cause Variation
Total Process
Common Cause
Special Cause
=
+
Variation
Variation
Variation
Common cause variation


naturally occurring and expected



the result of normal variation in
materials, tools, machines, operators,
and the environment

Prentice-Hall, Inc.

Chap 17-15

Special Cause Variation
Total Process
Common Cause
Special Cause
=
+
Variation
Variation
Variation
Special cause variation


abnormal or unexpected variation



has an assignable cause



variation beyond what is considered
inherent to the process

Prentice-Hall, Inc.

Chap 17-16

Control Limits
Forming the Upper control limit (UCL) and the
Lower control limit (LCL):
UCL = Process Average + 3 Standard Deviations
LCL = Process Average – 3 Standard Deviations
UCL
+3σ

Process Average

- 3σ

Prentice-Hall, Inc.

LCL
time

Chap 17-17

Control Chart Basics
Special Cause Variation:
Range of unexpected variability

UCL
Common Cause
Variation: range of
expected variability

+3σ

Process Average

- 3σ
LCL
time

Chap 17-18
Prentice-Hall, Inc.

Process Variability
Special Cause of Variation:
A measurement this far from the process average
is very unlikely if only expected variation is present

UCL
±3σ → 99.7% of
process values
should be in this
range

Process Average
LCL
time

Chap 17-19
Prentice-Hall, Inc.

Using Control Charts


Control Charts are used to check for process
control
H0: The process is in control
i.e., variation is only due to common causes

H1: The process is out of control
i.e., special cause variation exists

If the process is found to be out of control,
steps should be taken to find and eliminate the
special causes of variation


Prentice-Hall, Inc.

Chap 17-20

In-control Process


A process is said to be in control when the
control chart does not indicate any out-of-control
condition
 Contains only common causes of variation




If the common causes of variation is small, then
control chart can be used to monitor the process
If the common causes of variation is too large, you
need to alter the process

Prentice-Hall, Inc.

Chap 17-21

Process In Control


Process in control: points are randomly
distributed around the center line and all
points are within the control limits
UCL
Process Average
LCL

Prentice-Hall, Inc.

time

Chap 17-22

Process Not in Control
Out of control conditions:


One or more points outside control limits



8 or more points in a row on one side of the
center line



8 or more points moving in the same
direction

Prentice-Hall, Inc.

Chap 17-23

Process Not in Control


One or more points outside
control limits



Eight or more points in a row
on one side of the center line

UCL
Process
Average

Process
Average

LCL


UCL

LCL

Eight or more points moving in
the same direction
UCL
Process
Average

Statistics for ManagersLCL
Using
Prentice-Hall, Inc.

Chap 17-24

Out-of-control Processes


When the control chart indicates an out-ofcontrol condition (a point outside the control
limits or exhibiting trend, for example)




Contains both common causes of variation and
assignable causes of variation
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

Prentice-Hall, Inc.

Chap 17-25

Statistical Process Control Charts
Statistical
Process Control
Charts

p chart

X chart and R
chart

Used for
proportions
(attribute data)

Used for
measured
numeric data

Prentice-Hall, Inc.

Chap 17-26

p Chart


Control chart for proportions




Is an attribute chart

Shows proportion of nonconforming items


Example -- Computer chips: Count the number of
defective chips and divide by total chips inspected


Chip is either defective or not defective

Finding a defective chip can be classified a
“success”
Chap 17-27
Prentice-Hall, Inc.


p Chart
(continued)


Used with equal or unequal sample sizes
(subgroups) over time






Unequal sizes should not differ by more than ±25%
from average sample sizes
Easier to develop with equal sample sizes

Should have np > 5 and n(1 - p) > 5

Prentice-Hall, Inc.

Chap 17-28

Creating a p Chart


Calculate subgroup proportions



Graph subgroup proportions



Compute average proportion



Compute the upper and lower control limits



Add centerline and control limits to graph

Prentice-Hall, Inc.

Chap 17-29

p Chart Example
Subgroup
number

Sample
size

Number of
successes

Sample
Proportion, ps

1
2
3
…

150
150
150

15
12
17
…

10.00
8.00
11.33
…

Prentice-Hall, Inc.

Average
subgroup
proportion =

p

Chap 17-30

Average of Subgroup Proportions
The average of subgroup proportions = p
If equal sample sizes:

If unequal sample sizes:
k

k

p=

∑ pi
i=1

k

where:
pi = sample proportion
for subgroup i
k = number of subgroups
Microsoft size n 4e © 2004
of Excel,

Prentice-Hall, Inc.

p=

∑X
i=1
k

∑n
i =1

i

i

where:
Xi = the number of nonconforming
items in sample i
Σni = total number of items
sampled in k samples

Chap 17-31

Computing Control Limits


The upper and lower control limits for a p chart
are
UCL = Average Proportion + 3 Standard Deviations
LCL = Average Proportion – 3 Standard Deviations



The standard deviation for the subgroup
proportions is

(p)(1 − p)
n
Prentice-Hall, Inc.

Chap 17-32

(continued)


The upper and lower control limits for the
p chart are

p(1 − p)
UCL = p + 3
n
p(1 − p)
LCL = p − 3
n
Prentice-Hall, Inc.

Proportions are
never negative, so
if the calculated
lower control limit
is negative, set
LCL = 0

Chap 17-33

p Chart Example
You are the manager of a 500-room hotel.
You want to achieve the highest level of
service. For seven days, you collect data on
the readiness of 200 rooms. Is the process in
control?

Prentice-Hall, Inc.

Chap 17-34

p Chart Example:
Hotel Data
Day
1
2
3
4
5
6
7

# Rooms
200
200
200
200
200
200
200

Prentice-Hall, Inc.

# 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 17-35

p Chart
Control Limits Solution
k

p=

∑X
i=1
k

∑n
i =1

i

i

16 + 7 +  + 16
121
=
=
= .0864
200 + 200 +  + 200 1400
k

n=

∑n
i =1

k

i

200 + 200 +  + 200
=
= 200
7

p(1 − p)
.0864(1 − .0864 )
UCL = p + 3
= .0864 + 3
= .1460
200
n
p(1 − Using
Statistics for Managers p) = .0864 − 3 .0864(1 − .0864 ) = .0268
LCL = p − 3
200
Microsoft Excel, 4e © n
2004
Chap 17-36
Prentice-Hall, Inc.

p Chart
Control Chart Solution
P
0.15

UCL = .1460
_
p = .0864

0.10
0.05
0.00

LCL = .0268
1

2

3

4

5
Day

6
_

7

Individual points are distributed around p without any pattern.
Any improvement in the process must come from reduction
of common-cause variation,
Statistics for Managers Using which is the responsibility of
management.
Chap 17-37
Prentice-Hall, Inc.

Understanding Process Variability:
Red Bead Experiment
The experiment:
 From a box with 20% red beads and 80% white
beads, have “workers” scoop out 50 beads


Tell the workers their job is to get white beads



10 red beads out of 50 (20%) is the expected
value. Scold workers who get more than 10,
praise workers who get less than 10

Some workers will get better over time, some
will get 4e © 2004
Microsoft Excel,worse


Prentice-Hall, Inc.

Chap 17-38

Morals of the
Red Bead Experiment
2.

3.
4.

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.
proportion

1.

Subgroup number
Prentice-Hall, Inc.

UCL
p
LCL

Chap 17-39

R chart and X chart


Used for measured numeric data from a
process



Start with at least 20 subgroups of observed
values



Subgroups usually contain 3 to 6
observations each

For the process to be in control, both the R
Statisticschart and theUsing chart must be in control
for Managers X-bar


Prentice-Hall, Inc.

Chap 17-40

Example: Subgroups


Process measurements:
Subgroup measures

Subgroup Individual measurements
number
(subgroup size = 4)

1
2
3
…

15
12
17
…

17
16
21
…

15
9
18
…

Prentice-Hall, Inc.

11
15
20
…

Mean, X

Range, R

14.5
13.0
19.0
…

6
7
4
…

Average
subgroup
mean = X

Average
subgroup
range = R

Chap 17-41

The R Chart


Monitors variability in a process






The characteristic of interest is measured
on a numerical scale
Is a variables control chart

Shows the sample range over time


Range = difference between smallest and
largest values in the subgroup

Prentice-Hall, Inc.

Chap 17-42

Steps to create an R chart


Find the mean of the subgroup ranges (the
center line of the R chart)



for the R chart



Use lines to show the center and control
limits on the R chart

Plot the successive subgroup ranges as a
Statisticsline Managers Using
for chart


Prentice-Hall, Inc.

Chap 17-43

Average of Subgroup Ranges
Average of subgroup ranges:

∑R
R=

i

k

where:
Ri = ith subgroup range

Prentice-Hall, Inc.

Chap 17-44

R Chart Control Limits


The upper and lower control limits for an
R chart are

UCL = D 4 ( R )
LCL = D3 ( R )
where:
D4 and D3 are taken from the table
Managers Using E.11) for subgroup size = n
(Appendix Table

Statistics for
Prentice-Hall, Inc.

Chap 17-45

R Chart Example
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 variation
in the process in control?

Prentice-Hall, Inc.

Chap 17-46

R Chart Example:
Subgroup Data
Day
1
2
3
4
5
6
7

Subgroup Subgroup Subgroup
Size
Average
Range
5
5
5
5
5
5
5

Prentice-Hall, Inc.

5.32
6.59
4.89
5.70
4.07
7.34
6.79

3.85
4.27
3.28
2.99
3.61
5.04
4.22

Chap 17-47

R Chart Center and
Control Limits

∑R
R=
k

i

3.85 + 4.27 +  + 4.22
=
= 3.894
7

UCL = D 4 ( R ) = (2.114 )(3.894 ) = 8.232
LCL = D3 ( R ) = (0)(3.894 ) = 0
D4 and D3 are from
Table E.11 (n = 5)
Prentice-Hall, Inc.

Chap 17-48

R Chart
Minutes
UCL = 8.232

8
6
4
2
0

_
R = 3.894
LCL = 0
1

2

3

4
Day

5

6

7

Conclusion: Variation is in control
Chap 17-49
Prentice-Hall, Inc.

The X Chart


Shows the means of successive
subgroups over time



Monitors process average



Must be preceded by examination of the
R chart to make sure that the variation in
the process is in control

Prentice-Hall, Inc.

Chap 17-50

Steps to create an X chart


Compute the mean of the subgroup means
(the center line of the X chart)



for the X chart



Graph the subgroup means



Add the center line and control limits to the
graph

Prentice-Hall, Inc.

Chap 17-51

Average of Subgroup
Means
Average of subgroup means:

∑X
X=

i

k

where:
Xi = ith subgroup average

Prentice-Hall, Inc.

Chap 17-52



The upper and lower control limits for an X chart
are generally defined as



Use

R
d2 n

to estimate the standard deviation
of the process average, where d2
is from appendix Table E.11

Prentice-Hall, Inc.

Chap 17-53

(continued)


The upper and lower control limits for an X chart
are generally defined as



so

UCL = X + 3
LCL = X − 3

Prentice-Hall, Inc.

R
d2 n
R
d2 n
Chap 17-54

(continued)


Simplify the control limit calculations by using

UCL = X + A 2 ( R )
LCL = X − A 2 ( R )
where

A2 =

3
d2 n

Prentice-Hall, Inc.

Chap 17-55

X Chart Example
You want to analyze the time it takes to deliver
luggage to the room. For seven days, you
collect data on five deliveries per day. Is the
process average in control?

Prentice-Hall, Inc.

Chap 17-56

X Chart Example:
Subgroup Data
Day
1
2
3
4
5
6
7

Size
Average
Range
5
5
5
5
5
5
5

Prentice-Hall, Inc.

5.32
6.59
4.89
5.70
4.07
7.34
6.79

3.85
4.27
3.28
2.99
3.61
5.04
4.22

Chap 17-57

X Chart
Control Limits Solution
∑X
X=

i

k

∑R
R=
k

i

5.32 + 6.59 +  + 6.79
=
= 5.813
7
3.85 + 4.27 +  + 4.22
=
= 3.894
7

UCL = X + A 2 ( R ) = 5.813 + (0.577 )(3.894 ) = 8.060
LCL = X − A 2 ( R ) = 5.813 − (0.577 )(3.894 ) = 3.566
Prentice-Hall, Inc.

A2 is from Table
E.11 (n = 5)
Chap 17-58

X Chart
Minutes
8
6
4
2
0
1

UCL = 8.060
_
_
X = 5.813
LCL = 3.566
2

3

4
Day

5

6

7

Conclusion: Process average is in statistical control
Chap 17-59
Prentice-Hall, Inc.

Control Charts in PHStat
Use:


PHStat | control charts | p chart …



PHStat | control charts | R & XBar charts …

Prentice-Hall, Inc.

Chap 17-60

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 customers’ expectations
 The upper specification limit (USL) is the largest
value that can be obtained and still conform to
customers’ expectations
 The lower specification limit (LSL) is the
smallest value that
Statistics for Managers Using is still conforming


Prentice-Hall, Inc.

Chap 17-61

Estimating Process Capability


Must first have an in-control process



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 / d2

Prentice-Hall, Inc.

Chap 17-62

(continued)


For a characteristic with a LSL and a USL
P(outcome will be within specifications)




USL − X 
 LSL − X
= P(LSL < X < USL ) = P
<Z<

R
R


 d

d2
2



 Where Z is a standardized normal random variable
Chap 17-63
Prentice-Hall, Inc.

(continued)


For a characteristic with only an USL




USL − X 

= P( X < USL ) = P Z <

R




d2



Chap 17-64
Prentice-Hall, Inc.

(continued)


For a characteristic with only a LSL




 LSL − X

= P(LSL < X) = P
< Z
R


 d

2



Chap 17-65
Prentice-Hall, Inc.

Process Capability
Example
You have instituted a policy that 99% of all
luggage deliveries must be completed within
ten minutes or less. For seven days, you
collect data on five deliveries per day. You
know from prior analysis that the process is
in control. Is the process capable?

Prentice-Hall, Inc.

Chap 17-66

Process Capability:
Hotel Data
Day
1
2
3
4
5
6
7

Size
Average
Range
5
5
5
5
5
5
5

Prentice-Hall, Inc.

5.32
6.59
4.89
5.70
4.07
7.34
6.79

3.85
4.27
3.28
2.99
3.61
5.04
4.22

Chap 17-67

Process Capability:
Hotel Example Solution
n=5

X = 5.813

R = 3.894

d2 = 2.326




10 − 5.813 

= P( X < 10) = P Z <
3.894 



2.326 

= P( Z < 2.50) = .9938
Therefore, we estimate that 99.38% of the luggage deliveries
Statistics made within the ten minutes or less specification. The
will be for Managers Using
Microsoft Excel, 4e © of meeting the 99% goal.
process is capable 2004
Chap 17-68
Prentice-Hall, Inc.

Capability Indices


A process capability index is an aggregate
measure of a process’s ability to meet
specification limits



The larger the value, the more capable a
process is of meeting requirements

Prentice-Hall, Inc.

Chap 17-69

Cp Index


A measure of potential process performance
is the Cp index
USL − LSL specification spread
Cp =
=
process spread
6(R / d2 )

Cp > 1 implies a process has the potential of having
more than 99.73% of outcomes within
specifications
 C > 2 implies a process has the potential of
p
meeting the expectations set forth in six sigma
management
Chap 17-70
Prentice-Hall, Inc.


CPL and CPU


To measure capability in terms of actual
process performance:
X − LSL
CPL =
3(R / d2 )
CPU =

USL − X
3(R / d2 )

CPL (CPU) > 1 implies that the process mean is
more than 3 Using
Statistics for Managers standard deviation away from the lower
(upper) © 2004
Microsoft Excel, 4especification limit
Chap 17-71
Prentice-Hall, Inc.


CPL and CPU
(continued)


Used for one-sided specification limits


Use CPU when a characteristic only has a UCL



Use CPL when a characteristic only has an LCL

Prentice-Hall, Inc.

Chap 17-72

Cpk Index




The most commonly used capability index is the
Cpk index
Measures actual process performance for
characteristics with two-sided specification limits
Cpk = min(CPL, CPU)

Cpk = 1 indicates that the process average is 3
standard deviation away from the closest specification
limit
 Larger C indicates greater capability of meeting the
pk
Statistics for Managers Using > 2 indicates compliance with
requirements, e.g., Cpk
six sigma management
Chap 17-73
Prentice-Hall, Inc.


Process Capability
Example
You have instituted a policy that all luggage
deliveries must be completed within ten
minutes or less. For seven days, you collect
data on five deliveries per day. You know
from prior analysis that the process is in
control. Compute an appropriate capability
index for the delivery process.
Prentice-Hall, Inc.

Chap 17-74

Process Capability:
Hotel Example Solution
n=5

X = 5.813

R = 3.894

d2 = 2.326

USL − X
10 − 5.813
CPU =
=
= .833672
3(R / d2 ) 3(3.894 / 2.326 )

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 deviation Using
Statistics for Managers above the mean.
Chap 17-75
Prentice-Hall, Inc.

Chapter Summary


Reviewed the philosophy of quality management




Deming’s 14 points

Discussed Six Sigma® Management





Reduce defects to no more than 3.4 per million
Uses DMAIC model for process improvement

Discussed the theory of control charts


Common cause variation vs. special cause variation



Constructed and interpreted p charts



Constructed and interpreted X and R charts

Obtained and interpreted process capability measures
Chap 17-76
Prentice-Hall, Inc.


Chap17 statistical applications on management

Recommandé

Recommandé

Contenu connexe

Tendances

Tendances (19)

En vedette

En vedette (14)

Similaire à Chap17 statistical applications on management

Similaire à Chap17 statistical applications on management (20)

Plus de Uni Azza Aunillah

Plus de Uni Azza Aunillah (12)

Dernier

Dernier (20)

Chap17 statistical applications on management