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10s-1 Acceptance Sampling

William J. Stevenson

Operations Management

8th edition

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10s-2 Acceptance Sampling

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10s-3 Acceptance Sampling

Sampling Plans

Acceptance sampling: Form ofinspection applied to lots or batches ofitems before or after a process, to judgeconformance with predetermined

standards Sampling plans: Plans that specify lot

size, sample size, number of samples,and acceptance/rejection criteria

Single-sampling

Double-sampling

Multiple-sampling

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10s-4 Acceptance SamplingOperating CharacteristicCurve

00.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 .05 .10 .15 .20 .25Proba

bility

ofac

ceptin

g

lot

Lot quality (fraction defective)

3%

Figure 10S.1

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10s-5 Acceptance Sampling

Decision Criteria

0

1.00

Proba

bility

ofac

ceptin

g

lot

Lot quality (fraction defective)

Good Bad

Ideal

Not verydiscriminating

Figure 10S.2

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10s-6 Acceptance Sampling

Sampling Terms

Acceptance quality level (AQL): thepercentage of defects at which consumers arewilling to accept lots as good

Lot tolerance percent defective (LTPD): the

upper limit on the percentage of defects that aconsumer is willing to accept

Consumers risk: the probability that a lotcontained defectives exceeding the LTPD will beaccepted

Producers risk: the probability that a lotcontaining the acceptable quality level will berejected

C d d

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10s-7 Acceptance SamplingConsumers and ProducersRisk

00.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 .05 .10 .15 .20 .25Proba

bility

ofac

ceptin

g

lot

Lot quality (fraction defective)

= .10

= .10

Good

AQL

BadIndifferent

LTPD

Figure 10S.3

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10s-8 Acceptance Sampling

QC Curve for n = 10, c = 1QC Curve for n = 10, c = 1Figure 10S.4

00.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 .10 .20 .30 .40 .50Proba

bility

ofac

ceptance

Fraction defective in lot

.9139

.7361

.5443

.3758

.2440

.1493

.0860

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10s-9 Acceptance Sampling

Average Quality

Average outgoing quality (AOQ):Average of inspected lots (100%) and

uninspected lots AOQ Pac p

N n

N=

Pac = Probability of accepting lot

p = Fraction defective

N = Lot sizen = Sample size

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10s-10 Acceptance Sampling

Example 2: AOQ

0 0

0 .0 5 0 .0 4 6

0 .1 0 .0 7 4

0 .1 5 0 .0 8 2

0 .2 0 .0 7 5

0 .2 5 0 .0 6 1

0 .3 0 .0 4 5

0 .3 5 0 .0 3

0 .4 0 .0 1 9

0

0 . 0 1

0 . 0 2

0 . 0 3

0 . 0 4

0 . 0 5

0 . 0 6

0 . 0 7

0 . 0 8

0 . 0 9

0 0 . 0 5 0 . 1 0 . 1 5 0 . 2 0 . 2 5 0 . 3 0 . 3 5 0 . 4

Approximate AOQL = .082

AOQ(

Fractiondefec

tiveout)

Incoming fraction defective