Operations management by stevenson 9th ch10s

10S

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McGraw-Hill/Irwin

Copyright © 2007 by The McGraw-Hill Companies, Inc. All


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Operations Management

William J. Stevenson

8th edition
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CHAPTER

10s

Acceptance
Sampling

McGraw-Hill/Irwin

Operations Management, Eighth Edition, by William J. Stevenson
Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights

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Sampling Plans
 Acceptance sampling: Form of

inspection applied to lots or batches of
items before or after a process, to judge
conformance 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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Operating Characteristic Curve
Probability of accepting lot

Figure 10S.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

3%

0

.05

.10

.15

.20

.25

Lot quality (fraction defective)
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Decision Criteria

Probability of accepting lot

Figure 10S.2
1.00

Ideal

Not very
discriminating

“Good”

“Bad”

0

Lot quality (fraction defective)
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Sampling Terms
 Acceptance quality level (AQL): the

percentage of defects at which consumers are
willing to accept lots as “good”

 Lot tolerance percent defective (LTPD):
the upper limit on the percentage of defects
that a consumer is willing to accept

 Consumer’s risk: the probability that a lot

contained defectives exceeding the LTPD will
be accepted

 Producer’s risk: the probability that a lot

containing the acceptable quality level will be
rejected
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Consumer’s and Producer’s Risk
Probability of accepting lot

Figure 10S.3

1
α = .10
0.9
0.8
0.7
0.6

0.5
0.4
0.3
0.2 “Good” Indifferent
0.1
β = .10
0
0
.05
.10
AQL

LTPD
“Bad”

.15

.20

.25

Lot quality (fraction defective)
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QC Curve for n = 10, c = 1

Probability of acceptance

Figure 10S.4

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

.9139
.7361
.5443
.3758
.2440
.1493
.0860

0

.10

.20

.30

.40

.50

Fraction defective in lot
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Average Quality
 Average outgoing quality (AOQ):
Average of inspected lots (100%) and
uninspected lots
 N − n
AOQ = Pac × p

 N 

Pac = Probability of accepting lot
p = Fraction defective
N = Lot size
n = Sample size

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AOQ (Fraction defective out)

Example 2: AOQ
0
0.05
0.09
0.1

0.08
0.070.15
0.06 0.2
0.050.25
0.04 0.3
0.03
0.35
0.02
0.01 0.4

0
0.046
0.074
0.082
0.075
0.061
0.045
0.03
0.019

Approximate AOQL = .082

0
0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Incoming fraction defective

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