chapter 17 introduction to quality and statistical process control l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Chapter 17 Introduction to Quality and Statistical Process Control PowerPoint Presentation
Download Presentation
Chapter 17 Introduction to Quality and Statistical Process Control

Loading in 2 Seconds...

play fullscreen
1 / 55

Chapter 17 Introduction to Quality and Statistical Process Control - PowerPoint PPT Presentation


  • 497 Views
  • Uploaded on

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

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Chapter 17 Introduction to Quality and Statistical Process Control' - libitha


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
chapter 17 introduction to quality and statistical process control

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
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
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
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
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 points6
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 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
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
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
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
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
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
  • 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
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
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
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
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
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
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
p-Chart Example

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

average of subgroup proportions
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
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
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
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
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
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
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
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
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
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
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
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
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.