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Chapter 17 Introduction to Quality and Statistical Process Control

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## Chapter 17 Introduction to Quality and Statistical Process Control

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### Chapter 17Introduction to Quality and Statistical Process Control

A Decision-Making Approach

6th Edition

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

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

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

- 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

- 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.

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 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

- 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 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

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

- 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 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 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 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 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

- 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

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

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

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

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

- 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

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

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 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

- 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

- 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-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

- Process measurements:

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

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

- 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 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

- 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

UCL

x-chart

LCL

time

UCL

R-chart

LCL

time

Business Statistics: A Decision-Making Approach, 6e © 2005 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

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

- 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

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 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

- 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

- 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-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

- 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

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

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 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

- 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 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

- 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

- 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 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

The control limits for a c-chart are

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

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

- 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

- 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

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

- 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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