CD-ROM Chap 17-1 A Course In Business Statistics, 4th © 2006 Prentice-Hall, Inc. A Course In...

CD-ROM Chap 17-1A Course In Business Statistics, 4th © 2006 Prentice-Hall, Inc.

A Course In Business Statistics

4th Edition

CD-ROM Chapter 17Introduction to Quality and Statistical Process Control


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


Chapter Overview

Quality Management and Tools for Improvement

Deming’s 14 Points

Juran’s 10 Steps to Quality

Improvement

The Basic 7 Tools

Philosophy of Quality

Tools for Quality Improvement

Control Charts

X-bar/R-charts

p-charts

c-charts


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


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



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.

(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

(continued)



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


Juran’s 10 Steps to Quality Improvement

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

(continued)


The Deming Cycle

The Deming

CycleThe key is a continuous cycle of improvement

Act

Plan

Do

Study


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


The Basic 7 Tools


2. Brainstorming

3. Fishbone Diagram

4. Histogram

5. Trend Charts

6. Scatter Plots


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

(continued)


The Basic 7 Tools


2. Brainstorming

3. Fishbone Diagram

4. Histogram

5. Trend Charts

6. Scatter Plots


Cause 4Cause 3

Cause 2Cause 1

Problem

Fishbone (cause-and-effect) diagram:

Sub-causes

Sub-causes

Show patterns of variation

(continued)


The Basic 7 Tools


2. Brainstorming

3. Fishbone Diagram

4. Histogram

5. Trend Charts

6. Scatter Plots


time

y

x

y

Identify trend

Examine relationships

(continued)


The Basic 7 Tools


2. Brainstorming

3. Fishbone Diagram

4. Histogram

5. Trend Charts

6. Scatter Plots


X

Examine the performance of a process over time

time

(continued)


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


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


Sources of Variation




People Machines Materials Methods Measurement Environment

Variation is often due to differences in:






Common cause variation naturally occurring and expected the result of normal variation in

materials, tools, machines, operators, and the environment


Special Cause Variation




Special cause variation abnormal or unexpected variation has an assignable cause variation beyond what is considered

inherent to the process


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


Process Average

Control Chart Basics

UCL = Process Average + 3 Standard Deviations LCL = Process Average – 3 Standard Deviations

UCL

LCL

+3σ

- 3σ

Common Cause Variation: range of expected variability

Special Cause Variation: Range of unexpected variability

time


Process Average

Process Variability


UCL

LCL

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

time

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


Statistical Process Control Charts

Statistical Process Control

Charts

X-bar charts and R-charts

c-charts

Used for measured

numeric data

Used for proportions

(attribute data)

Used for number of

attributes per sampling unit

p-charts


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


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


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

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

(continued)


Example: x-chart

Process measurements:

Subgroup measuresSubgroup number Individual measurements Mean, x Range, R

1

2

3

…

15

12

17

…

17

16

21

…

15

9

18

…

11

15

20

…

14.5

13.0

19.0

…

6

7

4

…Average subgroup

mean = x

Average subgroup range = R


Average of Subgroup Means and Ranges

k

xx i

k

RR i

Average of subgroup means:

where:xi = ith subgroup average

k = number of subgroups

Average of subgroup ranges:

where:Ri = ith subgroup range

k = number of subgroups


Computing Control Limits

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

or


3

3

xLCL

xUCL



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

The value A2R is used to estimate 3σ , where A2 is from Appendix Q

The upper and lower control limits are

)R(AxLCL

)R(AxUCL

2

2

(continued)

where A2 = Shewhart factor for subgroup size n from appendix Q


Example: R-chart

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

)R(DLCL

)R(DUCL

3

4

where:D4 and D3 are taken from the Shewhart table(appendix Q) for subgroup size = n


x-chart and R-chart

UCL

LCL

time

x

UCL

LCL

time

RR-chart

x-chart


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

HA: 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


Process In Control

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

UCL

LCL

x

x

time


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


Process Not in Control

One or more points outside control limits

UCL

LCL

x


UCL

LCL

x


UCL

LCL

x


UCL

LCL

x


Out-of-control Processes

When the control chart indicates an out-of-control 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


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”


p-Chart

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

(continued)


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


p-Chart Example

Subgroup number

Sample size

Number of successes Proportion, p

1

2

3

…

150

150

150

15

12

17

…

10.00

8.00

11.33

…Average subgroup

proportion = p


Average of Subgroup Proportions

The average of subgroup proportions = p

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

where: ni = number of items in sample i ni = total number of items

sampled in k samples

If equal sample sizes: If unequal sample sizes:

k

pp i

i

ii

n

pnp



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

or

UCL = Average Proportion + 3 Standard Deviations LCL = Average Proportion – 3 Standard Deviations

3

3

pLCL

pUCL


Standard Deviation of Subgroup Proportions

The estimate of the standard deviation for the subgroup proportions is

n

)p)(1p(s

p

If equal sample sizes: If unequal sample sizes:

where: = mean subgroup

proportion n = common sample size

p

Generally, is computed separately for each different sample size

ps



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

(continued)

n

)p)(1p(pLCL

n

)p)(1p(pUCL

3

3

)s(pLCL

)s(pUCL

p

p

3

3

If sample sizes are equal, this becomes

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


p-Chart Examples

For equal sample sizes

For unequal sample sizes

UCL

LCL

UCL

LCL

p p

ps is constant since

n is the same for all subgroups

ps varies for each

subgroup since ni varies


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


Mean and Standard Deviationfor a c-Chart

The mean for a c-chart is

k

xc i

The standard deviation for a c-chart is

cs

where: xi = number of successes per sampling unit k = number of sampling units


c-Chart Control Limits

ccLCL

ccUCL

3

3

The control limits for a c-chart are


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: One or more points outside control limits





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 1 2 3 4 5 6 7

Flaws found 2 1 3 0 5 1 0


Constructing the c-Chart

The mean and standard deviation are:

1.71437

0150312

k

xc i

1.30931.7143cs

2.2143(1.3093)1.7143c3cLCL

5.6423(1.3093)1.7143c3cUCL

The control limits are:

Note: LCL < 0 so set LCL = 0


The completed c-Chart

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

UCL = 5.642

LCL = 0

Sample number1 2 3 4 5 6 7

c = 1.714

6

5

4

3

2

1

0


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

CD-ROM Chap 17-1 A Course In Business Statistics, 4th © 2006 Prentice-Hall, Inc. A Course In...

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