© 1997 prentice-hall, inc. s3 - 1 principles of operations management quality via statistical...

© 1997 Prentice-Hall, Inc.© 1997 Prentice-Hall, Inc.

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Principles of Principles of Operations ManagementOperations Management

Principles of Principles of Operations ManagementOperations Management

Quality Via Quality Via Statistical Process ControlStatistical Process Control

Chapter S3Chapter S3


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Learning ObjectivesLearning ObjectivesLearning ObjectivesLearning Objectives

Explain statistical process controlExplain statistical process control Develop control charts for variablesDevelop control charts for variables

RR chart, chart,XX chart chart

Develop control charts for attributesDevelop control charts for attributes PP chart, chart, cc chart chart


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Thinking ChallengeThinking ChallengeThinking ChallengeThinking Challenge

In the mid-1980’s, most firms In the mid-1980’s, most firms adjusted the process if output adjusted the process if output varied by varied by ± 3± 3 from average from average ((2,7002,700 defects per million defects per million products). In trouble, Motorola products). In trouble, Motorola decided to use decided to use ± 6± 6. This meant . This meant no more than no more than 22 defects per defects per billionbillion products. Should Motorola have products. Should Motorola have followed industry practice, used followed industry practice, used 66, or some other standard?, or some other standard?

© 1995 Corel Corp.

AloneAlone GroupGroup Class Class


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Statistical Statistical Quality Control (SQC)Quality Control (SQC)

Statistical Statistical Quality Control (SQC)Quality Control (SQC)

Uses mathematics (i.e., statistics)Uses mathematics (i.e., statistics) Involves collecting, organizing, & Involves collecting, organizing, &

interpreting data interpreting data Objective: Regulate product qualityObjective: Regulate product quality Used toUsed to

Control the process as products are Control the process as products are producedproduced

Inspect samples of finished productsInspect samples of finished products


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Types of Statistical Types of Statistical Quality ControlQuality Control

Types of Statistical Types of Statistical Quality ControlQuality Control

StatisticalQuality Control

ProcessControl

AcceptanceSampling

VariablesCharts

AttributesCharts

Variables Attributes

StatisticalQuality Control

ProcessControl

AcceptanceSampling

VariablesCharts

AttributesCharts

Variables Attributes


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Characteristics for Characteristics for which you focus on which you focus on defectsdefects

Classify products as Classify products as either ‘good’ or ‘bad’, either ‘good’ or ‘bad’, or count # defectsor count # defects e.g., radio works or note.g., radio works or not

Categorical or discrete Categorical or discrete random variablesrandom variables

AttributesAttributes

Quality CharacteristicsQuality CharacteristicsQuality CharacteristicsQuality Characteristics

Characteristics that Characteristics that you measureyou measure e.g., weight, lengthe.g., weight, length

May be whole May be whole number or fractionalnumber or fractional

Continuous random Continuous random variablesvariables

VariablesVariables


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Statistical Statistical Process Control (SPC)Process Control (SPC)

Statistical Statistical Process Control (SPC)Process Control (SPC)

Statistical technique used to ensure Statistical technique used to ensure process is making product to standardprocess is making product to standard

All process are subject to variabilityAll process are subject to variability Natural causesNatural causes: Random variations: Random variations Assignable causesAssignable causes: Correctable problems: Correctable problems

Machine wear, unskilled workers, poor mat’lMachine wear, unskilled workers, poor mat’l

Objective: Identify assignable causesObjective: Identify assignable causes Uses process control chartsUses process control charts


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0

20

40

60

1 3 5 7 9 11

X

Time

0

20

40

60

1 3 5 7 9 11

X

Time

Process Control ChartsProcess Control ChartsProcess Control ChartsProcess Control Charts

Graph of sample data plotted over timeGraph of sample data plotted over time

UCLUCL

LCLLCL

Assignable Assignable Cause Cause VariationVariation

Process Process Average Average ± 3± 3

Natural Natural VariationVariation


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Control Chart PurposesControl Chart PurposesControl Chart PurposesControl Chart Purposes

Show changes in data patternShow changes in data pattern e.g., trendse.g., trends

Make corrections Make corrections beforebefore process is out of process is out of controlcontrol

Show causes of changes in dataShow causes of changes in data Assignable causesAssignable causes

Data outside control limits or trend in dataData outside control limits or trend in data Natural causesNatural causes

Random variations around averageRandom variations around average


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X

Theoretical Basis Theoretical Basis of Control Chartsof Control ChartsTheoretical Basis Theoretical Basis of Control Chartsof Control Charts

As As sample sample size gets size gets large large enough enough (( 30) ... 30) ...

sampling sampling distribution distribution becomes becomes almost normal almost normal regardless of regardless of population population distribution.distribution.

Central Limit TheoremCentral Limit Theorem

XX


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Theoretical Basis Theoretical Basis of Control Chartsof Control ChartsTheoretical Basis Theoretical Basis of Control Chartsof Control Charts

Properties of normal distributionProperties of normal distribution

X X X

99.7% of all99.7% of allX X fall within ± 3fall within ± 3XX


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Produce GoodProvide Service

Stop Process

Yes

No

Assign.Causes?Take Sample

Inspect Sample

Find Out WhyCreate

Control Chart

StartProduce Good

Provide Service

Stop Process

Yes

No

Assign.Causes?Take Sample

Inspect Sample

Find Out WhyCreate

Control Chart

Start

Statistical Process Statistical Process Control StepsControl Steps

Statistical Process Statistical Process Control StepsControl Steps


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Control Chart TypesControl Chart TypesControl Chart TypesControl Chart Types

ControlCharts

RChart

VariablesCharts

AttributesCharts

XChart

PChart

CChart

ControlCharts

RChart

VariablesCharts

AttributesCharts

XChart

PChart

CChart

Continuous Continuous Numerical DataNumerical Data

Categorical or Categorical or Discrete Numerical Discrete Numerical DataData


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RR Chart ChartRR Chart Chart

Type of variables control chartType of variables control chart Interval or ratio scaled numerical dataInterval or ratio scaled numerical data

Shows sample ranges over timeShows sample ranges over time Difference between smallest & largest Difference between smallest & largest

values in inspection samplevalues in inspection sample

Monitors variability in processMonitors variability in process Example: Weigh samples of coffee & Example: Weigh samples of coffee &

compute ranges of samples; Plotcompute ranges of samples; Plot


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RR Chart Chart Control LimitsControl Limits

RR Chart Chart Control LimitsControl Limits

UCL D R

LCL D R

R

R

k

R

R

ii

k

4

3

1

UCL D R

LCL D R

R

R

k

R

R

ii

k

4

3

1

Sample Range Sample Range at Timeat Time i i

# Samples# Samples

From Table S3.1From Table S3.1


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RR Chart Chart ExampleExampleRR Chart Chart ExampleExample

You’re manager of a You’re manager of a 500-room hotel. You 500-room hotel. You want to analyze the want to analyze the time it takes to deliver time it takes to deliver luggage to the room. luggage to the room. For 7 days, you collect For 7 days, you collect data ondata on 5 5 deliveries deliveries per day. Is the per day. Is the process in controlprocess in control??


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RR & &XX Chart Chart Hotel DataHotel Data


SampleSampleDayDay Delivery TimeDelivery Time MeanMean RangeRange

11 7.307.30 4.204.20 6.106.10 3.453.45 5.555.55 5.325.32

7.30 + 4.20 + 6.10 + 3.45 + 5.557.30 + 4.20 + 6.10 + 3.45 + 5.55 5 5

Sample Mean = Sample Mean =


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11 7.307.30 4.204.20 6.106.10 3.453.45 5.555.55 5.325.32 3.853.85

7.30 - 3.457.30 - 3.45Sample Range = Sample Range =

LargestLargest SmallestSmallest


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11 7.307.30 4.204.20 6.106.10 3.453.45 5.555.55 5.325.32 3.853.8522 4.604.60 8.708.70 7.607.60 4.434.43 7.627.62 6.596.59 4.274.2733 5.985.98 2.922.92 6.206.20 4.204.20 5.105.10 4.884.88 3.283.2844 7.207.20 5.105.10 5.195.19 6.806.80 4.214.21 5.705.70 2.992.9955 4.004.00 4.504.50 5.505.50 1.891.89 4.464.46 4.074.07 3.613.6166 10.1010.10 8.108.10 6.506.50 5.065.06 6.946.94 7.347.34 5.045.0477 6.776.77 5.085.08 5.905.90 6.906.90 9.309.30 6.796.79 4.224.22


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RR

RR

RR Chart Chart Control Limits SolutionControl Limits Solution


From Table From Table S3.1 (S3.1 (nn = 5) = 5)

RR

kk

UCLUCL DD

iiii

kk

RR

11

44

33 8585 44 2727 44 2222

7733 894894

22 114114 33 894894 88 232232

.. .. ....

.. .. ..

LL


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Partial Table for Partial Table for Control Chart LimitsControl Chart Limits

Partial Table for Partial Table for Control Chart LimitsControl Chart Limits

n A2 D4 D3

2 1.880 3.268 0

3 1.023 2.574 0

4 0.729 2.282 0

5 0.577 2.114 0

6 0.483 2.004 0

7 0.419 1.924 0.076

n A2 D4 D3

2 1.880 3.268 0

3 1.023 2.574 0

4 0.729 2.282 0

5 0.577 2.114 0

6 0.483 2.004 0

7 0.419 1.924 0.076


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R

R

k

UCL D R

LCL D R

ii

k

R

R

1

4

3

3 85 4 27 4 227

3 894

2114 3 894 8 232

0 3 894 0

. . ..

. . .

.

a fa fafa f

R

R

k

UCL D R

LCL D R

ii

k

R

R

1

4

3

3 85 4 27 4 227

3 894

2114 3 894 8 232

0 3 894 0

. . ..

. . .

.

a fa fafa f


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02468

1 2 3 4 5 6 7

R, Minutes

Day

02468

1 2 3 4 5 6 7

R, Minutes

Day

02468

1 2 3 4 5 6 7

R, Minutes

Day

RR Chart Chart Control Chart SolutionControl Chart Solution

RR Chart Chart Control Chart SolutionControl Chart Solution

UCLUCL


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XX Chart ChartXX Chart Chart

Type of variables control chartType of variables control chart Interval or ratio scaled numerical dataInterval or ratio scaled numerical data

Shows sample means over timeShows sample means over time Monitors process averageMonitors process average Example: Weigh samples of coffee & Example: Weigh samples of coffee &

compute means of samples; Plotcompute means of samples; Plot


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XX Chart Chart Control LimitsControl Limits

XX Chart Chart Control LimitsControl Limits

UCL X A R

LCL X A R

X

X

kR

R

k

X

X

ii

k

ii

k

2

2

1 1

UCL X A R

LCL X A R

X

X

kR

R

k

X

X

ii

k

ii

k

2

2

1 1

Sample Sample Range Range at Timeat Time i i

# Samples# Samples

Sample Sample Mean at Mean at Time Time ii

From From Table S3.1Table S3.1


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11 7.307.30 4.204.20 6.106.10 3.453.45 5.555.55 5.325.32 3.853.8522 4.604.60 8.708.70 7.607.60 4.434.43 7.627.62 6.596.59 4.274.2733 5.985.98 2.922.92 6.206.20 4.204.20 5.105.10 4.884.88 3.283.2844 7.207.20 5.105.10 5.195.19 6.806.80 4.214.21 5.705.70 2.992.9955 4.004.00 4.504.50 5.505.50 1.891.89 4.464.46 4.074.07 3.613.6166 10.1010.10 8.108.10 6.506.50 5.065.06 6.946.94 7.347.34 5.045.0477 6.776.77 5.085.08 5.905.90 6.906.90 9.309.30 6.796.79 4.224.22


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XX Chart Chart Control Limits SolutionControl Limits Solution**

XX Chart Chart Control Limits SolutionControl Limits Solution**

X

X

k

R

R

k

UCL X A R

LCL X A R

ii

k

ii

k

X

X

1

1

2

2

5 32 6 59 6 797

5 813

3 85 4 27 4 227

3 894

5 813 0 577 3 894 8 060

5 813 0 577 3 894 3 566

. . ..

. . ..

. . . .

. . . .

a fa fa fa f

X

X

k

R

R

k

UCL X A R

LCL X A R

ii

k

ii

k

X

X

1

1

2

2

5 32 6 59 6 797

5 813

3 85 4 27 4 227

3 894

5 813 0 577 3 894 8 060

5 813 0 577 3 894 3 566

. . ..

. . ..

. . . .

. . . .

a fa fa fa f

From Table From Table S3.1 (S3.1 (nn = 5) = 5)


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XX Chart ChartControl Chart Solution*Control Chart Solution*

XX Chart ChartControl Chart Solution*Control Chart Solution*

02468

1 2 3 4 5 6 7

X, Minutes

Day

02468

1 2 3 4 5 6 7

X, Minutes

Day

UCLUCL

LCLLCL


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Thinking ChallengeThinking ChallengeThinking ChallengeThinking Challenge

You’re manager of a You’re manager of a 500-room hotel. The 500-room hotel. The hotel owner tells you hotel owner tells you that it takes too long to that it takes too long to deliver luggage to the deliver luggage to the room (even if the room (even if the process may be in process may be in control). What do you control). What do you do?do?

© 1995 Corel Corp.

AloneAlone GroupGroup Class Class


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pp Chart Chartpp Chart Chart

Type of attributes control chartType of attributes control chart Nominally scaled categorical dataNominally scaled categorical data

e.g., good-bade.g., good-bad

Shows % of nonconforming itemsShows % of nonconforming items Example: Count # defective chairs & Example: Count # defective chairs &

divide by total chairs inspected; Plotdivide by total chairs inspected; Plot Chair is either defective or not defectiveChair is either defective or not defective


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cc Chart Chartcc Chart Chart

Type of attributes control chartType of attributes control chart Discrete quantitative dataDiscrete quantitative data

Shows number of nonconformities Shows number of nonconformities (defects) in a unit (defects) in a unit Unit may be chair, steel sheet, car etc.Unit may be chair, steel sheet, car etc. Size of unit must be constantSize of unit must be constant

Example: Count # defects (scratches, Example: Count # defects (scratches, chips etc.) in chips etc.) in eacheach chair of a sample chair of a sample of 100 chairs; Plotof 100 chairs; Plot


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What Is What Is Acceptance Sampling?Acceptance Sampling?

What Is What Is Acceptance Sampling?Acceptance Sampling?

Form of quality testing used for Form of quality testing used for incoming materials or finished goodsincoming materials or finished goods e.g., purchased material & componentse.g., purchased material & components

ProcedureProcedure Take one or more samples at random Take one or more samples at random

from a lot (shipment) of itemsfrom a lot (shipment) of items Inspect each of the items in the sampleInspect each of the items in the sample Decide whether to reject the whole lot Decide whether to reject the whole lot

based on the inspection resultsbased on the inspection results


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What Is an What Is an Acceptance Plan?Acceptance Plan?

What Is an What Is an Acceptance Plan?Acceptance Plan?

Set of procedures for inspecting Set of procedures for inspecting incoming materials or finished goodsincoming materials or finished goods

IdentifiesIdentifies Type of sampleType of sample Sample size (Sample size (nn)) Criteria (Criteria (cc) used to reject or accept a lot) used to reject or accept a lot

Producer (supplier) & consumer Producer (supplier) & consumer (buyer) must negotiate(buyer) must negotiate


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Producer’s & Producer’s & Consumer’s RiskConsumer’s Risk

Producer’s & Producer’s & Consumer’s RiskConsumer’s Risk

Producer's risk (Producer's risk ()) Probability of rejecting a good lot Probability of rejecting a good lot Probability of rejecting a lot when Probability of rejecting a lot when

fraction defective is AQLfraction defective is AQL

Consumer's risk (ß)Consumer's risk (ß) Probability of accepting a bad lot Probability of accepting a bad lot Probability of accepting a lot when Probability of accepting a lot when

fraction defective is LTPDfraction defective is LTPD


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ConclusionConclusionConclusionConclusion

Explained statistical process controlExplained statistical process control Developed control charts for variablesDeveloped control charts for variables

RR chart, chart,XX chart chart

Discussed control charts for attributesDiscussed control charts for attributes PP chart, chart, cc chart chart

Explained acceptance samplingExplained acceptance sampling Producer’s & consumer’s riskProducer’s & consumer’s risk

© 1997 prentice-hall, inc. s3 - 1 principles of operations management quality via statistical...

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statistical process

x chart n

control chart purposes

defects n

n categorical

standard n

x slide

statistics n