ch 3 sup

1. 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
EditionOperations Management - 6th
Edition
Chapter 3 SupplementChapter 3 Supplement
Roberta Russell & Bernard W. Taylor, III
Acceptance SamplingAcceptance Sampling

2. Copyright 2009 John Wiley & Sons, Inc. Supplement 3-2
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

3. Copyright 2009 John Wiley & Sons, Inc. Supplement 3-3
Acceptance SamplingAcceptance Sampling
 Accepting or rejecting a production lot basedAccepting 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 DefectsNot consistent with TQM or Zero Defects
philosophyphilosophy

producer and customer agree on the number ofproducer 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

4. Copyright 2009 John Wiley & Sons, Inc. Supplement 3-4
Single–SampleSingle–Sample
Attribute PlanAttribute Plan
Single sampling plan
N = lot size
n = sample size (random)
c = acceptance number
d = number of defective items in sample
If d ≤ c, accept lot; else reject

5. Copyright 2009 John Wiley & Sons, Inc. Supplement 3-5
Producer’s andProducer’s and
Consumer’s RiskConsumer’s Risk
 AQL or acceptable quality levelAQL or acceptable quality level
 proportion of defects consumer will accept inproportion of defects consumer will accept in
a given lota given lot
 αα or producer’s riskor producer’s risk
 probability of rejecting a good lotprobability of rejecting a good lot
 LTPD or lot tolerance percent defectiveLTPD or lot tolerance percent defective
 limit on the number of defectives thelimit on the number of defectives the
customer will acceptcustomer will accept
 ββ or consumer’s riskor consumer’s risk
 probability of accepting a bad lotprobability of accepting a bad lot

6. Copyright 2009 John Wiley & Sons, Inc. Supplement 3-6
Producer’s andProducer’s and
Consumer’s Risk (cont.)Consumer’s Risk (cont.)
Sampling Errors
GoodLotGoodLotBadLotBadLot
AcceptAccept RejectReject
No Error
Type I Error
Producer’ Risk
Type II Error
Consumer’s Risk
No Error

7. Copyright 2009 John Wiley & Sons, Inc. Supplement 3-7
Operating CharacteristicOperating Characteristic
(OC) Curve(OC) Curve
 shows probability of accepting lots ofshows probability of accepting lots of
different quality levels with a specificdifferent quality levels with a specific
sampling plansampling plan
 assists management to discriminateassists management to discriminate
between good and bad lotsbetween good and bad lots
 exact shape and location of the curve isexact 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
planplan

8. Copyright 2009 John Wiley & Sons, Inc. Supplement 3-8
OC Curve (cont.)OC Curve (cont.)
OC curve forOC curve for nn andand cc
Proportion defectiveProportion defective
AQLAQL LTPDLTPD
Probabilityofacceptance,Probabilityofacceptance,PaPa
ββ = 0.10= 0.10
αα = 0.05= 0.05
1.001.00 –
0.800.80 –
0.600.60 –
0.400.40 –
0.200.20 –
–
|
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

9. Copyright 2009 John Wiley & Sons, Inc. Supplement 3-9
Developing a Sampling PlanDeveloping 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?
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 = 0.10
AQL = 1%
LTPD = 5%
N = 10,000 n = ?
α = 0.05 c = ?
β = 0.10
AQL = 1%
LTPD = 5%

10. Copyright 2009 John Wiley & Sons, Inc. Supplement 3-10
Average OutgoingAverage Outgoing
Quality (AOQ)Quality (AOQ)
 Expected number of defectiveExpected number of defective
items that will pass on toitems that will pass on to
customer with a sampling plancustomer with a sampling plan
 Average outgoing quality limitAverage outgoing quality limit
(AOQL)(AOQL)
 maximum point on the curvemaximum point on the curve

worst level of outgoing qualityworst level of outgoing quality

11. Copyright 2009 John Wiley & Sons, Inc. Supplement 3-11
AOQ CurveAOQ Curve

12. Copyright 2009 John Wiley & Sons, Inc. Supplement 3-12
Double-Sampling PlansDouble-Sampling Plans
 Take small initial sampleTake small initial sample
 If # defective lower limit, accept≤If # defective lower limit, accept≤
 If # defective > upper limit, rejectIf # defective > upper limit, reject
 If # defective between limits, take secondIf # 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

13. Copyright 2009 John Wiley & Sons, Inc. Supplement 3-13
Multiple-Sampling PlansMultiple-Sampling Plans
 Uses smaller sample sizesUses smaller sample sizes
 Take initial sampleTake initial sample
 If # defective lower limit, accept≤If # 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 rejectContinue sampling until accept or reject
lot based on all sample datalot based on all sample data

14. Copyright 2009 John Wiley & Sons, Inc. Supplement 3-14
Copyright 2009 John Wiley & Sons, Inc.Copyright 2009 John Wiley & Sons, Inc.
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