17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights...

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17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights

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Transcript of 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights...

Page 1: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 1

Chapter

Seventeen

McGraw-Hill/Irwin

© 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

Page 2: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 2

Chapter Seventeen

Statistical Quality

ControlGOALSWhen you have completed this chapter, you will be able to:ONEDiscuss the role of quality control in production and service operations.

TWO Define and understand the terms chance causes, assignable cause, in control and out of control, and variable.

THREEConstruct and interpret a Pareto chart.

FOURConstruct and interpret a Fishbone diagram.

Goals

Page 3: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 3

Chapter Seventeen continued

Statistical Quality ControlStatistical Quality ControlGOALSWhen you have completed this chapter, you will be able to:

FIVEConstruct and interpret a mean chart and a range chart.

SIX Construct and interpret a percent defective chart and a c-bar chart.

SEVENDiscuss acceptance sampling.

EIGHTConstruct an operating characteristic curve for various sampling plans.

Goals

Page 4: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 4

Statistical Process Control

A collection of strategies, techniques, and actions taken by an organization to ensure they

are producing a quality product or providing a quality service

Statistical Process Control Statistical Process Control

Page 5: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 5

Causes of Variation

Assignable VariationAssignable Variation is not random in nature and can be reduced or eliminated by investigating the problem and finding the cause.

There is variation in all parts produced by a manufacturing process.

Sources of VariationSources of Variation

Chance VariationChance Variation is random in nature and cannot be entirely eliminated.

Page 6: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 6

A technique for tallying the number and type of defects that happen within a product or service

Produce a vertical bar chart to display data.

Diagnostic Charts: Pareto Chart

Pareto AnalysisPareto Analysis

Steps in pareto analysisSteps in pareto analysis

Tally the type of defects.

Rank the defects in terms of frequency of occurrence from largest to smallest.

Page 7: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 7The accounting department of a large organization is spending significant time correcting travel vouchers submitted by employees from its numerous locations. Accounting staff noted that typical errors included wrong travel codes, incorrect employee identification numbers, inaccurate math, placing expenses on the wrong lines of the form, and failure to include proper documentation of expenses. Example 1

Department staff pulled a sample of 100 vouchers and tallied errors in the various categories.

Page 8: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 8

Error Type Number found

Wrong codes 60

Incorrect employee identification number

25

Inaccurate math 23

Inaccurate form placement

80

Incomplete documentation

42

Example 1 continued

Page 9: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 9

Error Type Number Percent

Wrong codes 60 26

Incorrect employee identification number

25 11

Inaccurate math 23 10

Inaccurate form placement

80 35

Incomplete documentation

42 18

Total 330 100

Example 1 Pareto table

Page 10: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 10

Pareto Chart for Voucher Errors

0

10

20

30

40

50

60

70

80

90

Inaccurate formplacement

Wrong codes Incompletedocumentation

Incorrect employeeid

Inaccurate math

Defect

Cou

nt

-

10

20

30

40

50

60

70

80

90

100

Cum

ulat

ive P

erce

ntEXCEL

Example 1 Pareto Chart

Page 11: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 11

Major causes listed on left-hand

side of diagram

Diagnostic Fishbone ChartDiagnostic Fishbone Chart

Also called cause-and-effect diagramcause-and-effect diagram

Helps organize ideas and identify

relationships

Identifies factors that

cause variability

Usually considers four problem areas: methods, materials,

equipment, and personnel

Problem or effect is head of fish

Fishbone chart

Page 12: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 12

Suppose a family restaurant, such as those found along an interstate highway, has recently been experiencing complaints from customers that the food being served is cold.

Example 2

In the following fishbone diagram, notice each of the subcauses are listed as assumptions. Each of these subcauses must be investigated to find the real problem regarding the cold food.

Page 13: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 13

Methods

Equipment Personnel

Materials

Complaintsof cold

food

Food placed underheating lights

Food heated tocorrect temperature Food at correct

starting tem perature

Packaging insulatesenough

Thermostatworking properly

Heating lights atcorrect height

Em ployees operatingequipm ent correctly

Servers deliverfood quickly

Example 2

Page 14: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 14

Purpose of Quality Control Charts

Portray graphically when an assignable cause enters the production system so that it can be identified and corrected

Monitoring accomplished by periodically selecting a random sample from the current production.

Purpose of Quality-Control Charts

Page 15: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 15

Types of Quality Control Charts-Variables

Xwhere is the mean of the sample means

Mean (Mean (xx-bar) Chart-bar) Chart

Designed to control variables such as weight or length

Limits How much variation can be expected for a given sample size

UCL: upper control limitLCL: lower control limit

U C L = X + 3 s

nL C L = X - 3

s

n

Page 16: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 16

UCL X A R and LCL X A R 2 2

is the mean of the sample rangesR

Xwhere is the mean of the sample means

Shortcut method for UCL and LCL

A2 is a constant used in computing the

upper and lower control limits, factors found in Appendix B.

Shortcut method

Page 17: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 17

Types of Quality Control Charts-Variables

UCL D R and LCL D R 4 3

Designed to show whether the overall range of measurements is in or out of control

Range ChartRange Chart

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17- 18

Example 3

Hour #mm. #mm. #mm. #mm.

1 23 24 26 28

2 26 24 30 27

3 24 32 26 27

4 24 28 31 26

5 25 24 25 27

A manufacturer of chair wheels wishes to maintain the quality of the manufacturing process. Every 15 minutes, for a five hour period, a wheel is selected and the diameter measured. Given are the diameters (in mm.) of the wheels.

Page 19: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 19

EXAMPLE 3 continued

Hour X R1 25.3 52 26.8 63 27.3 84 27.3 75 25.3 3

Mean and Range Table

Grand Mean (25.25+26.75+...+25.25)

5 = 26.35

Mean Range

(5+6+...+3)

5

=5.8

UCL and LCL for MeanUCL=26.35+.729(5.8)=30.58LCL=26.35-.729(5.8)=22.12

UCL and LCL for the range diameter UCL=2.282(5.8) = 13.24

LCL=2.282(0) = 0

Page 20: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 20

UCL = 30.58

Mean Chart for Diameters

20

22

24

26

28

30

1 2 3 4 5Hours

Sa

mp

le M

ea

ns

Mean=26.35

LCL=22.12

UCL=30.58

Example 3 continued

No points outside limits: Process in control

Page 21: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 21

Range Charts for Diameters

0

2

4

6

8

10

12

14

1 2 3 4 5

Hour

Sa

mp

le R

an

ge

UCL = 13.24

Mean =5.8

LCL = 0

Example 3 continued

No points outside limits: Process in control

Page 22: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 22

Types of Quality Control Charts-Attributes

samplesofNumber

defectivespercenttheofSump

Percent Defective ChartPercent Defective Chart((pp-chart or -chart or pp-bar chart)-bar chart)

Graphically shows the proportion of the production that is not acceptable (p)

The UCLUCL and LCLLCL computed as the mean percent defective plus or minus 3 times the standard error of the percents

n

pppLCLandUCL

)1(3

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17- 23

Example 4

.. ( . )

. .

08 308 1 08

40008 041

A manufacturer of running shoes wants to establish control limits for the percent defective. Ten samples of 400 shoes revealed the mean percent defective was 8.0% Where should the manufacturer set the control limits?

Page 24: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 24

Types of Quality Control Charts-Attributes

UCL and LCL c c 3

CC-chart (-chart (cc-bar chart) -bar chart)

UCL and LCL found byDesigned to monitor the number of defects per

unit

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17- 25

Example 5

84.46.2

6.236.2

6.210/26

LCLandUCL

c

A manufacturer of computer circuit boards tested 10 after they were manufactured. The number of defects obtained per circuit board were: 5, 3, 4, 0, 2, 2, 1, 4, 3, and 2. Construct the appropriate control limits.

Page 26: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 26

c-bar chart for Number of Defects per Circuit Board

012345678

1 2 3 4 5 6 7 8 9 10

Sample Number

Sa

mp

le C

ou

nt

UCL = 7.44

c = 2.6

LCL = 0

Example 5

Page 27: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 27

Acceptance Sampling

c is the maximum number of defective units that may be found in the

sample for the lot to still be considered acceptable.

Acceptance samplingAcceptance sampling

A method of determining whether an incoming lot of a product meets specified

standards

Based on random sampling

techniques

A random sample of n units is obtained from the

entire lot.

Page 28: 17- 1 Chapter Seventeen McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

17- 28

736.387.349.)10.,10/1(

914.315.599.)05.,10/1(

nXP

nXP

Suppose a manufacturer and a supplier agree on a sampling plan with n=10 and acceptance number of 1. What is the probability of accepting a lot with 5% defective? A lot with 10% defective?

Uses binomial probability distribution to determine the probabilities of accepting lots of various quality levels

Operating Characteristic Curve

Short form OC

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17- 29

OC Curve for Sampling Plan (n=20,c=2)

0

0.2

0.4

0.6

0.8

1

1.2

0 10 20 30 40

Incoming lot percent defective

Pro

ba

bili

ty o

f a

cc

ep

tin

g lo

tProbability of

accepting a lot that is 10%

defectiveis .677

Example 6


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