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Business Statistics: A Decision-Making Approach 6 th Edition Chapter 17 Introduction 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

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Chapter 17 introduction to quality and statistical process control l.jpg

Business Statistics:

A Decision-Making Approach

6th Edition

Chapter 17Introduction to Quality and Statistical Process Control

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


Chapter goals l.jpg
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

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


Chapter overview l.jpg
Chapter Overview

Quality Management and Tools for Improvement

Tools for Quality Improvement

Philosophy of Quality

Deming’s 14 Points

The Basic 7 Tools

Control Charts

Juran’s 10 Steps to Quality Improvement

X-bar/R-charts

p-charts

c-charts

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


Themes of quality management l.jpg
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

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


Deming s 14 points l.jpg
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

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


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Deming’s 14 Points

(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.

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


Deming s 14 points7 l.jpg
Deming’s 14 Points

(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

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


Juran s 10 steps to quality improvement l.jpg
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

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


Juran s 10 steps to quality improvement9 l.jpg
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

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


The deming cycle l.jpg
The Deming Cycle

Plan

The

Deming

Cycle

Act

Do

The key is a continuous cycle of improvement

Study

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


The basic 7 tools l.jpg
The Basic 7 Tools

  • Process Flowcharts

  • Brainstorming

  • Fishbone Diagram

  • Histogram

  • Trend Charts

  • Scatter Plots

  • Statistical Process Control Charts

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


The basic 7 tools12 l.jpg
The Basic 7 Tools

(continued)

  • Process Flowcharts

  • Brainstorming

  • Fishbone Diagram

  • Histogram

  • Trend Charts

  • Scatter Plots

  • Statistical Process Control Charts

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

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


The basic 7 tools13 l.jpg
The Basic 7 Tools

(continued)

  • Process Flowcharts

  • Brainstorming

  • Fishbone Diagram

  • Histogram

  • Trend Charts

  • Scatter Plots

  • Statistical Process Control Charts

Fishbone (cause-and-effect) diagram:

Cause 1

Cause 2

Sub-causes

Problem

Sub-causes

Cause 4

Cause 3

Show patterns of variation

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


The basic 7 tools14 l.jpg
The Basic 7 Tools

(continued)

  • Process Flowcharts

  • Brainstorming

  • Fishbone Diagram

  • Histogram

  • Trend Charts

  • Scatter Plots

  • Statistical Process Control Charts

Identify trend

y

time

Examine relationships

y

x

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


The basic 7 tools15 l.jpg
The Basic 7 Tools

(continued)

  • Process Flowcharts

  • Brainstorming

  • Fishbone Diagram

  • Histogram

  • Trend Charts

  • Scatter Plots

  • Statistical Process Control Charts

Examine the performance of a process over time

X

time

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


Introduction to control charts l.jpg
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

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


Process variation l.jpg
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

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


Sources of variation l.jpg
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

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


Common cause variation l.jpg
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

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


Special cause variation l.jpg
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

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


Statistical process control charts l.jpg
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

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


Control chart basics l.jpg
Control Chart Basics

Special Cause Variation:

Range of unexpected variability

UCL

Common Cause Variation: range of expected variability

+3σ

Process Average

-3σ

LCL

time

UCL = Process Average + 3 Standard Deviations

LCL = Process Average – 3 Standard Deviations

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


Process variability l.jpg
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

UCL = Process Average + 3 Standard Deviations

LCL = Process Average – 3 Standard Deviations

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


Statistical process control charts24 l.jpg
Statistical Process Control Charts

Statistical Process Control Charts

X-bar charts and R-charts

p-charts

c-charts

Used for measured numeric data

Used for proportions (attribute data)

Used for number of attributes per sampling unit

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


X bar chart and r chart l.jpg
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

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


Steps to create an x chart and an r chart l.jpg
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

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


Steps to create an x chart and an r chart27 l.jpg
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

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


Example x chart l.jpg
Example: x-chart

  • Process measurements:

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


Average of subgroup means and ranges l.jpg
Average of Subgroup Means and Ranges

Average of

subgroup means:

Average of

subgroup ranges:

where:

xi = ith subgroup average

k = number of subgroups

where:

Ri = ith subgroup range

k = number of subgroups

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


Computing control limits l.jpg
Computing Control Limits

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

  • or

UCL = Process Average + 3 Standard Deviations

LCL = Process Average – 3 Standard Deviations

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


Computing control limits31 l.jpg
Computing Control Limits

(continued)

  • 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

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

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


Example r chart l.jpg
Example: R-chart

  • The upper and lower control limits for an

    R-chart are

where:

D4 and D3 are taken from the Shewhart table

(appendix Q) for subgroup size = n

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


X chart and r chart l.jpg
x-chart and R-chart

UCL

x-chart

LCL

time

UCL

R-chart

LCL

time

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


Using control charts l.jpg
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

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


Process in control l.jpg
Process In Control

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

UCL

LCL

time

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


Process not in control l.jpg
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 movingin the same direction

  • 14 or more points alternating above and below the center line

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


Process not in control37 l.jpg
Process Not in Control

  • One or more points outside control limits

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

UCL

UCL

LCL

LCL

  • Six or more points moving in the same direction

  • 14 or more points alternating above and below the center line

UCL

UCL

LCL

LCL

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


Out of control processes l.jpg
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

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


P chart l.jpg
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”

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


P chart40 l.jpg
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

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


Creating a p chart l.jpg
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

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


P chart example l.jpg
p-Chart Example

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


Average of subgroup proportions l.jpg
Average of Subgroup Proportions

The average of subgroup proportions = p

If equal sample sizes:

If unequal sample sizes:

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

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


Computing control limits44 l.jpg
Computing Control Limits

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

  • or

UCL = Average Proportion + 3 Standard Deviations

LCL = Average Proportion – 3 Standard Deviations

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


Standard deviation of subgroup proportions l.jpg
Standard Deviation of Subgroup Proportions

  • The estimate of the standard deviation for the subgroup proportions is

If equal sample sizes:

If unequal sample sizes:

Generally, is computed separately for each different sample size

where:

= mean subgroup proportion

n = common sample size

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


Computing control limits46 l.jpg
Computing Control Limits

(continued)

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

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

  • If sample sizes are equal, this becomes

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


P chart examples l.jpg
p-Chart Examples

  • For equal sample sizes

  • For unequal sample sizes

UCL

UCL

p

p

LCL

LCL

is constant since n is the same for all subgroups

varies for each subgroup since ni varies

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


C chart l.jpg
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

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


Mean and standard deviation for a c chart l.jpg
Mean and Standard Deviationfor a c-Chart

  • The mean for a c-chart is

  • The standard deviation for a c-chart is

where:

xi = number of successes per sampling unit

k = number of sampling units

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


C chart control limits l.jpg
c-Chart Control Limits

The control limits for a c-chart are

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


Process control l.jpg
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

  • 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

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


C chart example l.jpg
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

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


Constructing the c chart l.jpg
Constructing the c-Chart

  • The mean and standard deviation are:

  • The control limits are:

Note: LCL < 0 so set LCL = 0

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


The completed c chart l.jpg
The completed c-Chart

6

5

4

3

2

1

0

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

c = 1.714

LCL = 0

1 2 3 4 5 6 7

Sample number

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


Chapter summary l.jpg
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

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


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