Chapter 17 Student Lecture Notes 17-1

Chapter 17 Student Lecture Notes

Business Statistics:

A Decision-Making Approach

6 th Edition

Chapter 17

Introduction to Quality and

Statistical Process Control

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.

Chap 17-1

Chapter Goals

After completing this chapter, you should be able to:

Use the seven basic tools of quality

Construct and interpret x-bar and R-charts

Construct and interpret p-charts

Construct and interpret c-charts


Chap 17-2

Chapter Overview

Quality Management and

Tools for Improvement

Philosophy of

Quality

Tools for Quality

Improvement

Deming’s 14

Points

Juran’s 10

Steps to

Quality

Improvement


The Basic

7 Tools

Control

Charts

X-bar/R-charts p-charts c-charts

Chap 17-3

Business Statistics: A Decision-Making Approach, 6e

17-1

© 2005 Prentice-Hall, Inc.


Themes of Quality Management

Primary focus is on process improvement

Most variations in process are due to systems

Teamwork is integral to quality management

Customer satisfaction is a primary goal

Organization transformation is necessary

It is important to remove fear

Higher quality costs less


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 to build long-run purchaser/supplier relationships


Chap 17-5


(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 between departments so that people can work as a team.


Chap 17-6


17-2




(continued)

10. Eliminate slogans and targets for the workforce

They can create adversarial relationships

11. Eliminate quotas and management by objectives

12. Remove barriers to pride of workmanship

13. Institute a vigorous program of education and self-improvement

14. Make the transformation everyone’s job


Chap 17-7

Juran’s 10 Steps to Quality

Improvement

1. Build awareness of both the need for improvement and the opportunity for improvement

2. Set goals for improvement

3. Organize to meet the goals that have been set

4. Provide training

5. Implement projects aimed at solving problems


Chap 17-8

Juran’s 10 Steps to Quality

Improvement

(continued)

6. Report progress

7. Give recognition

8. Communicate the results

9. Keep score

10. Maintain momentum by building improvement into the company’s regular systems


Chap 17-9


17-3



The Deming Cycle

Plan

Act

The

Deming

Cycle

Study


Do

The key is a continuous cycle of improvement

Chap 17-10

The Basic 7 Tools

1. Process Flowcharts

2. Brainstorming

3. Fishbone Diagram

4. Histogram

5. Trend Charts

6. Scatter Plots

7. Statistical Process

Control Charts


Chap 17-11

1.

Process Flowcharts

2.

Brainstorming

3.

Fishbone Diagram

4.

Histogram

5.

Trend Charts

6.

Scatter Plots

7.

Statistical Process

Control Charts

The Basic 7 Tools

(continued)

Map out the process to better visualize and understand opportunities for improvement


Chap 17-12


17-4



The Basic 7 Tools

(continued)

Fishbone (cause-and-effect) diagram:

1.


2.

Brainstorming

3.


4.

Histogram

5.

Trend Charts

6.

Scatter Plots

7.


Control Charts

Cause 1

Sub-causes

Cause 2

Sub-causes

Problem

Cause 3 Cause 4

Show patterns of variation


Chap 17-13

The Basic 7 Tools

1.


2.

Brainstorming

3.


4.

Histogram

5.

Trend Charts

6.

Scatter Plots

7.


Control Charts

Examine relationships y y

Identify trend

(continued) time


x

Chap 17-14

1.


2.

Brainstorming

3.


4.

Histogram

5.

Trend Charts

6.

Scatter Plots

7.


Control Charts

The Basic 7 Tools

Examine the performance of a process over time

X

(continued) time


Chap 17-15


17-5



Introduction to Control Charts

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

Exhibits trend

Can make correction before process is out of control

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

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


Chap 17-16

Process Variation

Total Process

Variation

=

Common Cause

Variation

+

Special Cause

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 17-17

Sources of Variation

Total Process

Variation

=

Common Cause

Variation

+

Special Cause

Variation

Variation is often due to differences in:

People

Machines

Materials

Methods

Measurement

Environment


Chap 17-18


17-6



Common Cause Variation

Total Process

Variation

=

Common Cause

Variation

+

Special Cause

Variation

Common cause variation

naturally occurring and expected

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


Chap 17-19

Special Cause Variation

Total Process

Variation

=

Common Cause

Variation

+

Special Cause

Variation

Special cause variation

abnormal or unexpected variation

has an assignable cause variation beyond what is considered inherent to the process


Chap 17-20

Statistical Process 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

Common causes or chance

Inherent random variations

Consist of numerous small causes of random variability


Chap 17-21


17-7



Control Chart Basics

Special Cause Variation:

Range of unexpected variability

UCL

Common Cause

Variation: range of expected variability

+3 σ

-3 σ

Process Average

LCL time

UCL = Process Average + 3 Standard Deviations

LCL = Process Average – 3 Standard Deviations


Chap 17-22

Process Variability

Special Cause of Variation:

A measurement this far from the process average is very unlikely if only expected variation is present

UCL

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

Process Average

LCL time




Chap 17-23

Statistical Process Control Charts

Statistical

Process Control

Charts

X-bar charts and R-charts

Used for measured numeric data p-charts

Used for proportions

(attribute data) c-charts

Used for number of attributes per sampling unit


Chap 17-24


17-8



x-bar chart and R-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


Chap 17-25

Steps to create an x-chart and an R-chart

Calculate subgroup means and ranges

Compute the average of the subgroup means and the average range value

Prepare graphs of the subgroup means and ranges as a line chart


Chap 17-26

Steps to create an x-chart and an R-chart

(continued)

Compute the upper and lower control limits for the x-bar chart

Compute the upper and lower control limits for the R-chart

Use lines to show the control limits on the x-bar and R-charts


Chap 17-27


17-9



Example: x-chart

Process measurements:

Subgroup measures

Subgroup number

Individual measurements

1

2

3

15

12

17

17

16

21

15

9

18

11

15

20

… … … … …

Mean, x

14.5

13.0

19.0

…

Average subgroup mean = x

Range, R

6

7

4

…

Average subgroup range = R


Chap 17-28

Average of Subgroup

Means and Ranges

Average of subgroup means: x =

∑ k x i where: x i

= i th subgroup average k = number of subgroups

Average of subgroup ranges:

R =

∑

k

R i where:

R i

= i th subgroup range k = number of subgroups


Chap 17-29

Computing Control Limits

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



or

UCL = x +

3

σ

LCL = x −

3

σ


Chap 17-30


17-10




(continued)

Since control charts were developed before it was easy to calculate σ , the interval was formed using R instead

The value A

2

A

2

R is used to estimate 3 σ , where is from Appendix Q

The upper and lower control limits are

UCL

LCL

=

=

x x

+

A

2

( R )

−

A

2

( R ) where A

2

= Shewhart factor for subgroup size n from appendix Q


Chap 17-31

Example: R-chart

The upper and lower control limits for an

R-chart are

UCL

LCL

= D

4

( R )

= D

3

( R ) where:

D

4 and D

3 are taken from the Shewhart table

(appendix Q) for subgroup size = n


Chap 17-32 x-chart

R-chart

x-chart and R-chart

UCL x

LCL time

UCL

R

LCL time


Chap 17-33


17-11



Using Control Charts

Control Charts are used to check for process control

H

0

: The process is in control i.e., variation is only due to common causes

H

A

: 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


Chap 17-34

Process In Control

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

UCL x

LCL time


Chap 17-35

Process Not in Control

Out of control conditions:

One or more points outside control limits

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

Six or more points moving in the same direction

14 or more points alternating above and below the center line


Chap 17-36


17-12



Process Not in Control


UCL x

LCL


UCL x

LCL


UCL x

LCL



UCL x

LCL

Chap 17-37

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


Chap 17-38

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 17-39


17-13



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


Chap 17-40

Creating a p-Chart

Calculate subgroup proportions

Compute the average of the subgroup proportions

Prepare graphs of the subgroup proportions as a line chart

Compute the upper and lower control limits

Use lines to show the control limits on the p-chart


Chap 17-41

p-Chart Example

Subgroup number

1

2

3

…

Sample size

150

150

150

Number of successes

15

12

17

…

Proportion, p

10.00

8.00

11.33

…

Average subgroup proportion = p


Chap 17-42


17-14



Average of Subgroup Proportions

The average of subgroup proportions = p

If equal sample sizes: If unequal sample sizes: p

=

∑ k p i p

=

∑

∑ n i n i p i where: p i

= sample proportion for subgroup i k = number of subgroups of size n where: n i

Σ n

= number of items in sample i i

= total number of items sampled in k samples

Chap 17-43 Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.


The upper and lower control limits for an p-chart are

UCL = Average Proportion + 3 Standard Deviations

LCL = Average Proportion – 3 Standard Deviations

or

UCL = p +

3

σ

LCL = p −

3

σ


Chap 17-44

Standard Deviation of

Subgroup Proportions

The estimate of the standard deviation for the subgroup proportions is

If equal sample sizes: If unequal sample sizes: s p

=

( p )(1 − p ) n where: p

= mean subgroup proportion n = common sample size


computed separately for each different sample size

Chap 17-45


17-15




(continued)

The upper and lower control limits for the p-chart are

UCL

LCL

=

= p p

+

+

3

3

( s

( s p p

)

) Proportions are never negative, so if the calculated lower control limit is negative, set

LCL = 0

If sample sizes are equal, this becomes

UCL = p +

3

LCL = p −

3

( p )(1 − p ) n

( p )(1 − p ) n


Chap 17-46

p-Chart Examples

For equal sample sizes

For unequal sample sizes

UCL p

LCL

UCL p

LCL n is the same for all subgroups


subgroup since n i varies

Chap 17-47

c-Chart

Control chart for number of nonconformities

(occurrences) per sampling unit (an area of opportunity)

Also a type of attribute chart

Shows total number of nonconforming items per unit

examples: number of flaws per pane of glass number of errors per page of code

Assume that the size of each sampling unit remains constant


Chap 17-48


17-16



Mean and Standard Deviation for a c-Chart

The mean for a c-chart is c =

∑

k x i

The standard deviation for a c-chart is where: x i

= number of successes per sampling unit k = number of sampling units s = c


Chap 17-49

c-Chart Control Limits

The control limits for a c-chart are

UCL = c +

3

LCL = c −

3 c c


Chap 17-50

Process Control

Determine process control for p-chars and c-charts using the same rules as for x-bar and R-charts

Out of control conditions:






Chap 17-51


17-17



c-Chart Example

A weaving machine makes cloth in a standard width.

Random samples of 10 meters of cloth are examined for flaws.

Is the process in control?

Sample number

Flaws found

1

2

2

1

3

3

4

0

5

5

6

1

7

0


Chap 17-52

Constructing the c-Chart

The mean and standard deviation are: c =

∑ k x i =

2 + 1 + 3 + 0

7

+ 5 + 1 + 0

= 1.7143

s = c = 1.7143

= 1.3093

The control limits are:

UCL = c + 3

LCL = c − 3 c = 1.7143

+ 3(1.3093) = 5.642

c = 1.7143

+ 3(1.3093) = − 2.214

Note: LCL < 0 so set LCL = 0


Chap 17-53

The completed c-Chart

2

1

0

6

5

4

3

UCL = 5.642

c = 1.714

LCL = 0

1 2 3 4 5 6 7

Sample number

The process is in control. Individual points are distributed around the center line without any pattern. Any improvement in the process must come from reduction in common-cause variation


Chap 17-54


17-18



Chapter Summary

Reviewed the philosophy of quality management

Demings 14 points

Juran’s 10 steps

Described the seven basic tools of quality

Discussed the theory of control charts

Common cause variation vs. special cause variation

Constructed and interpreted x-bar and R-charts

Constructed and interpreted p-charts

Constructed and interpreted c-charts


Chap 17-55

17-19


Chapter 17 Student Lecture Notes 17-1

Business Statistics:

A Decision-Making Approach

Chapter 17

Introduction to Quality and

Statistical Process Control

Chapter Goals

Chapter Overview

Themes of Quality Management

Deming’s 14 Points

Deming’s 14 Points

Deming’s 14 Points

Juran’s 10 Steps to Quality

Improvement

Juran’s 10 Steps to Quality

Improvement

The Deming Cycle

Plan

Act

The

Deming

Cycle

Study

Do

The Basic 7 Tools

The Basic 7 Tools

The Basic 7 Tools

The Basic 7 Tools

The Basic 7 Tools

Introduction to Control Charts

Process Variation

Sources of Variation

Common Cause Variation

Special Cause Variation

Statistical Process Control Charts

Control Chart Basics

Process Variability

Statistical Process Control Charts

x-bar chart and R-chart

Steps to create an x-chart and an R-chart

Steps to create an x-chart and an R-chart

Example: x-chart

Average of Subgroup

Means and Ranges

∑

Computing Control Limits

Computing Control Limits

=

=

+

−

Example: R-chart

x-chart and R-chart

Using Control Charts

Process In Control

Process Not in Control

Process Not in Control

Out-of-control Processes

p-Chart

p-Chart

Creating a p-Chart

p-Chart Example

Average of Subgroup Proportions

Computing Control Limits

Standard Deviation of

Subgroup Proportions

Computing Control Limits

p-Chart Examples

c-Chart

Mean and Standard Deviation for a c-Chart

∑

c-Chart Control Limits

Process Control

c-Chart Example

Constructing the c-Chart

The completed c-Chart

Chapter Summary

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