Lecture Fundamentals of operations management (4/e): Chapter 9 - Davis, Aquilano, Chase

Chapter 6 Quality control tools for improving processes, after studying this chapter you will be able to: Introduce the different quality control tools that are used in analyzing and improving the quality of processes, describe in detail the two major approaches (that is, acceptance sampling and statistical process control) in which statistical analysis can be used to improve process quality, define the two different types of errors that can occur when statistical sampling is used,...

Quality Control Tools for  Improving Processes

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supplement 6

DAVIS AQUILANO CHASE

PowerPoint Presentation by Charlie Cook

Management 4e 

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S6–2

Supplement Objectives

Supplement Objectives

• Introduce the different quality control tools that are

used in analyzing and improving the quality of

processes

• Describe in detail the two major approaches (that is, acceptance sampling and statistical process control) in which statistical analysis can be used to improve

process quality

• Define the two different types of errors that can occur when statistical sampling is used

• Distinguish between attributes and variables with

respect to the statistical analysis of processes

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S6–4

The Basic Quality Control Tools

The Basic Quality Control Tools

• Seven Basic Quality Control (QC) Tools

–Process flowcharts (or diagrams)

–Bar charts and histograms

–Pareto charts

–Scatterplots (or diagrams)

–Run (or trend) charts

–Cause-and-effect (or fishbone) charts

–Statistical process control

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S6–5

Checksheet for Recording Complaints

Checksheet for Recording Complaints

Exhibit S6.1

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S6–6

Checksheet for Group Sizes in a Restaurant

Checksheet for Group Sizes in a Restaurant

Exhibit S6.2

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S6–7

Bar Chart of Daily Units Produced

Bar Chart of Daily Units Produced

Exhibit S6.3

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S6–8

Histogram of Hole Diameters

Histogram of Hole Diameters

Exhibit S6.4

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S6–9

Pareto Chart of Factors in an Emergency Room

Pareto Chart of Factors in an Emergency Room

Exhibit S6.5

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S6–10

Scatterplot of Customer Satisfaction and  Waiting Time in an Upscale Restaurant

Scatterplot of Customer Satisfaction and 

Waiting Time in an Upscale Restaurant

Exhibit S6.6

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S6–11

Run Chart of the Number of Daily Errors

Run Chart of the Number of Daily Errors

Exhibit S6.7

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S6–12

Cause­and­Effect Diagram for  Customer Complaints in a Restaurant

Cause­and­Effect Diagram for  Customer Complaints in a Restaurant

Exhibit S6.8

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S6–13

Statistical Analysis of Processes

Statistical Analysis of Processes

• Statistical Analysis

–Requires less labor (reduces costs)

–Useful when testing destroys products

• Categories of Statistical Tools

–Acceptance sampling

• Assesses the quality of parts or products after they

have been produced.

–Statistical process control

• Assesses whether or not an ongoing process is

performing within established limits.

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• Data that measure of a particular product characteristic

such as length or width.

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S6–15

Statistical Quality Control Methods

Statistical Quality Control Methods

Exhibit S6.9

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S6–16

Sampling Errors

Sampling Errors

• Type I (α Error or Producer’s Risk)

–Occurs when a sample says part are bad or the

process is out of control when the opposite is true.

–The probability of rejecting good parts as scrap.

• Type II (β error or Consumer’s Risk)

–Occurs when a sample says parts are good or

the process is in control when the reverse is

true.

–The probability of a customer getting a bad lot

represented as good.

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S6–17

Types of Sampling Errors

Types of Sampling Errors

Exhibit S6.10

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S6–18

Acceptance Sampling

Acceptance Sampling

• Designing a Sampling Plan for Attributes

–Costs to justify inspection

• Costs of not inspecting must exceed costs of

inspecting.

–Purposes of sampling plan

• Find quality or ensure quality is what it is supposed to

be.

–Acceptable quality level (AQL)

• Maximum percentage of defects that a company is

willing to accept.

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S6–19

Attribute Sampling

Attribute Sampling

• Defining an Attribute Sampling Plan

–N: number of units in the lot

–n: number of units in the sample

–c: the acceptance number (the maximum

number of defectives allowed in the sample before the whole lot is rejected.

• LTPD

–Lot tolerance percentage defective: the

percentage of defective units that can be in a single lot.

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S6–21

Operating Characteristic Curves

Operating Characteristic Curves

• Operating Characteristic (OC) Curves

–Curves that illustrate graphically the probability

of accepting lots that contain different percent defectives.

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–Points on an acceptance sampling chart that

distinguish the accept and reject region(s).

–Also, the points on a process control chart that

distinguish between a process being in or out of control.

• Factors to Consider in Designing a Plan

–The probability of rejecting a good lot (α error) –The probability of accepting bad lot (β error)

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S6–26

Statistical Process Control

Statistical Process Control

• Statistical Process Control (SPC)

–A quantitative method for determining whether a

particular process is in or out of control.

• Central Limit Theorem

–Sample means will be normally distributed no

matter what the shape of the distribution.

• Variation

–Random variation

–Nonrandom (assignable) variation

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S6–27

Areas Under the Normal Distribution Curve Corresponding to Different Numbers of Standard Deviation from the Mean

Areas Under the Normal Distribution Curve Corresponding to Different Numbers of Standard Deviation from the Mean

Exhibit S6.15

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S6–28

Control Chart Evidence for Investigation

Control Chart Evidence for Investigation

Exhibit S6.16a

Source: Bertrand L Hansen, Quality Control: Theory and Applications, © 1963, p

65 Reprinted by permission of Prentice Hall, Inc., Englewood Cliffs, NJ.

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S6–29

Control Chart Evidence for Investigation (cont’d)

Control Chart Evidence for Investigation (cont’d)

Exhibit S6.16b

Source: Bertrand L Hansen, Quality Control: Theory and Applications, © 1963, p

65 Reprinted by permission of Prentice Hall, Inc., Englewood Cliffs, NJ.

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S6–30

SPC Using Attribute Measurements

SPC Using Attribute Measurements

• Calculating Control Limits

–The centerline for an attribute chart is the

long-run average for the attribute in question.

• p-chart: percent defective chart

Centerline = p = Long-run average

Standard deviation of sample =

Upper control limit = UCL= p 3 sp

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S6–32

Constructing  X­bar  Charts

Constructing  X­bar  Charts

• X-bar Chart

–A chart that tracks the changes in the means of

the samples by plotting the means that were

taken from a process.

n

X X

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S6–33

Constructing  R  Charts

Constructing  R  Charts

• R Chart

–A chart that tracks the change in the variability

by plotting the range within each sample The range is the difference between the lowers and highest values in that sample.

m

R R

m

Total number of samples

Difference between the highest

and lowest values in sample j

Average of the measurement

differences R for all samples

m

 R j

R

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S6–34 Exhibit S6.17

Note: All factors based on the normal distribution.

Source: E L Grant, Statistical Quality Control, 6th ed (New York:

McGraw-Hill, 1988) Reprinted by permission of McGraw-Hill, Inc

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S6–35

Exhibit S6.18

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X

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S6–38

Six Sigma

Six Sigma

• Process Capability

–A comparison of control chart limits to design

specification limits to determine if the process itself is (or is not) capable of making products within design specification (or tolerance) limits.

–Process capability ratio

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S6–39

Six Sigma

Six Sigma

• Capability Index

–A calculation to determine how well the process

is performing relative to the target dimensions:

is the process closer to the upper specification limit (USL) or the lower specification limit (LSL)

–Capability Index

s

X

USL s

min

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*Tolerance: The range within which all individual measurements of units produced is desired to fall.

Source: Robert W Hall, Attaining Manufacturing Excellence: Just-in-Time Manufacturing, Total Quality, Total People

Involvement (Homewood, IL: Dow Jones-Irwin, 1987), p 66 By permission of The McGraw-Hill Companies.

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S6–41

Reducing Process Variance So that All Parts  Are within Specification (Tolerance)* (cont’d)

Reducing Process Variance So that All Parts  Are within Specification (Tolerance)* (cont’d)

Exhibit S6.21b

*Tolerance: The range within which all individual measurements of units produced is desired to fall.

Source: Robert W Hall, Attaining Manufacturing Excellence: Just-in-Time Manufacturing, Total Quality, Total People

Involvement (Homewood, IL: Dow Jones-Irwin, 1987), p 66 By permission of The McGraw-Hill Companies.

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S6–42

The Goal of Six Sigma

The Goal of Six Sigma

Exhibit S6.22

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S6–43

Impact of 1.5  Shift on 3  Process Impact of 1.5  Shift on 3  Process

Exhibit S6.23a

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S6–44

Impact of 1.5  Shift on 6  Process Impact of 1.5  Shift on 6  Process

Exhibit S6.23b

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S6–45

Defect Rates for Different Levels of  Sigma ( ) Assuming a 1.5 Shift in  Actual Mean from Design Mean

Defect Rates for Different Levels of  Sigma ( ) Assuming a 1.5 Shift in  Actual Mean from Design Mean

Exhibit S6.24

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S6–46

Taguchi Methods

Taguchi Methods

• Taguchi Methods

–Used for identifying the cause(s) of process

variation that reduces the number of tests that are necessary.

–Use to conduct experiments to determine the

best combinations of product and process

variables to make a product at the lowest cost with the highest uniformity.

–Quality loss function

• Relates the cost of quality directly to variation in a

process.

• Any deviation from target quality is a loss to society.

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S6–47

A Traditional View of the Cost of Variability

A Traditional View of the Cost of Variability

Exhibit S6.25

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S6–48

Taguchi’s View of the Cost of Variability

Taguchi’s View of the Cost of Variability

Exhibit S6.26

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S6–49 Exhibit CS6.1

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S6–50 Exhibit CS6.2

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S6–51 Exhibit CS6.3a

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S6–52 Exhibit CS6.3b

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S6–53 Exhibit CS6.3c

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S6–54 Exhibit CS6.4b