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Copyright 2009 John Wiley & Sons, Inc.Copyright 2009 John Wiley & Sons, Inc.Beni AsllaniBeni Asllani

University of Tennessee at ChattanoogaUniversity of Tennessee at Chattanooga

Operations Management - 6th Edition

Chapter 3 SupplementChapter 3 Supplement

Roberta Russell & Bernard W. Taylor, III

Acceptance SamplingAcceptance Sampling

Copyright 2009 John Wiley & Sons, Inc.Copyright 2009 John Wiley & Sons, Inc. Supplement 3-Supplement 3-22

Lecture OutlineLecture Outline

Single-Sample Attribute PlanSingle-Sample Attribute Plan Operating Characteristic CurveOperating Characteristic Curve Developing a Sampling Plan with ExcelDeveloping a Sampling Plan with Excel Average Outgoing QualityAverage Outgoing Quality Double - and Multiple-Sampling PlansDouble - and Multiple-Sampling Plans


Acceptance SamplingAcceptance Sampling

Accepting or rejecting a production lot based Accepting or rejecting a production lot based on the number of defects in a sampleon the number of defects in a sample

Not consistent with TQM or Zero Defects Not consistent with TQM or Zero Defects philosophyphilosophy producer and customer agree on the number of producer and customer agree on the number of

acceptable defectsacceptable defects a means of identifying not preventing poor qualitya means of identifying not preventing poor quality percent of defective parts versus PPMpercent of defective parts versus PPM

Sampling planSampling plan provides guidelines for accepting a lotprovides guidelines for accepting a lot


Single–Sample Single–Sample Attribute PlanAttribute Plan

Single sampling planN = lot sizen = sample size (random)c = acceptance numberd = number of defective items in sample

If d ≤ c, accept lot; else reject


Producer’s and Producer’s and Consumer’s RiskConsumer’s Risk

AQL or acceptable quality levelAQL or acceptable quality level proportion of defects consumer will accept in proportion of defects consumer will accept in

a given lota given lot or producer’s riskor producer’s risk

probability of rejecting a good lot probability of rejecting a good lot LTPD or lot tolerance percent defectiveLTPD or lot tolerance percent defective

limit on the number of defectives the limit on the number of defectives the customer will acceptcustomer will accept

ββ or consumer’s risk or consumer’s risk probability of accepting a bad lotprobability of accepting a bad lot


Producer’s and Producer’s and Consumer’s Risk (cont.)Consumer’s Risk (cont.)

Sampling Errors

Goo

d Lo

tG

ood

Lot

Bad

Lot

Bad

Lot

AcceptAccept RejectReject

No Error Type I ErrorProducer’ Risk

Type II ErrorConsumer’s Risk No Error


Operating Characteristic Operating Characteristic (OC) Curve(OC) Curve

shows probability of accepting lots of shows probability of accepting lots of different quality levels with a specific different quality levels with a specific sampling plansampling plan

assists management to discriminate assists management to discriminate between good and bad lotsbetween good and bad lots

exact shape and location of the curve is exact shape and location of the curve is defined by the sample size (defined by the sample size (nn) and ) and acceptance level (acceptance level (cc) for the sampling ) for the sampling plan plan


OC Curve (cont.)OC Curve (cont.)

OC curve for OC curve for n n and and cc

Proportion defectiveProportion defectiveAQLAQL LTPDLTPD

Prob

abili

ty o

f acc

epta

nce,

Pr

obab

ility

of a

ccep

tanc

e, P

aPa

= 0.10= 0.10

= 0.05= 0.051.00 1.00 –

0.80 0.80 –

0.60 0.60 –

0.40 0.40 –

0.20 0.20 –

–|

0.020.02|

0.040.04|

0.060.06|

0.080.08|

0.100.10|

0.120.12|

0.140.14|

0.160.16|

0.180.18|

0.200.20


Developing a Sampling Plan Developing a Sampling Plan with OM Toolswith OM Tools

ABC Company produces mugs in lots of 10,000. Performance measures for quality of mugs sent to stores call for a producer’s risk of 0.05 with an AQL of 1% defective and a consumer’s risk of 0.10 with a LTPD of 5% defective. What size sample and what acceptance number should ABC use to achieve performance measures called for in the sampling plan?

N = 10,000 n = ?α = 0.05 c = ?β = 0.10AQL = 1%LTPD = 5%


Average Outgoing Average Outgoing Quality (AOQ)Quality (AOQ)

Expected number of defective Expected number of defective items that will pass on to items that will pass on to customer with a sampling plancustomer with a sampling plan

Average outgoing quality limit Average outgoing quality limit (AOQL)(AOQL) maximum point on the curvemaximum point on the curve worst level of outgoing qualityworst level of outgoing quality


AOQ CurveAOQ Curve


Double-Sampling PlansDouble-Sampling Plans

Take small initial sampleTake small initial sample If # defective ≤ lower limit, acceptIf # defective ≤ lower limit, accept If # defective > upper limit, rejectIf # defective > upper limit, reject If # defective between limits, take second If # defective between limits, take second

samplesample Accept or reject based on 2 samplesAccept or reject based on 2 samples Less costly than single-sampling plansLess costly than single-sampling plans


Multiple-Sampling PlansMultiple-Sampling Plans

Uses smaller sample sizesUses smaller sample sizes Take initial sampleTake initial sample

If # defective ≤ lower limit, acceptIf # defective ≤ lower limit, accept If # defective > upper limit, rejectIf # defective > upper limit, reject If # defective between limits, resampleIf # defective between limits, resample

Continue sampling until accept or reject Continue sampling until accept or reject lot based on all sample datalot based on all sample data


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