Chap010s - Acceptance Sampling

10s-1

Acceptance Sampling

Operations Management

William J. Stevenson

8th edition S P CHHEDA & CO

10s-2

Acceptance Sampling

S P CHHEDA & CO

10s-3

Acceptance Sampling

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 S P CHHEDA & CO

Operating Characteristic Curve Figure 10S.1 Acceptance Sampling

Probability of accepting lot

10s-4

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

Lot quality (fraction defective) S P CHHEDA & CO

.25

10s-5

Acceptance Sampling

Decision Criteria Probability of accepting lot

Figure 10S.2

1.00

Ideal

Not very discriminating

“Good”

“Bad”

0

Lot quality (fraction defective) S P CHHEDA & CO

10s-6

Acceptance Sampling

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 S P CHHEDA & CO

Consumer’s and Producer’s Risk Figure 10S.3 Acceptance Sampling

Probability of accepting lot

10s-7

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

Lot quality (fraction defective) S P CHHEDA & CO

.25

10s-8

Acceptance Sampling

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

Fraction defective in lot S P CHHEDA & CO

.40

.50

10s-9

Acceptance Sampling

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

S P CHHEDA & CO

10s-10 Acceptance Sampling

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

Incoming fraction defective

S P CHHEDA & CO

0.4