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10S10S

Acceptance Sampling

10S-2

Learning ObjectivesLearning Objectives

Explain the purpose of acceptance sampling Contrast acceptance sampling and process

control Compare and contrast single- and multiple-

sampling plans Determine the average outgoing quality of

inspected lots

10S-3

Acceptance SamplingAcceptance Sampling Acceptance sampling: Form of inspection

applied to lots or batches of items before or after a process, to judge conformance with predetermined standards

10S-4

Acceptance SamplingAcceptance Sampling

Acceptance sampling is most useful when A large number of items must be processed in a

short time The cost consequences of passing defects are

low Destructive testing is required Fatigue or boredom leads to inspection errors

10S-5

Sampling PlansSampling Plans Plans that specify lot size, sample size,

number of samples, and acceptance/rejection criteria

Types of plans: Single-sampling Double-sampling Multiple-sampling

10S-6

Operating Characteristic CurveOperating Characteristic Curve

Operating Characteristic (OC) Curve: Probability curve that shows the probabilities of accepting lots with various fractions defective.

10S-7

Typical OC CurveTypical OC Curve

00.10.20.30.40.50.60.70.80.9

1

0 .05 .10 .15 .20 .25

Prob

abili

ty o

f acc

eptin

g lo

t

Lot quality (fraction defective)

3%

Figure 10S.1

10S-8

Decision CriteriaDecision Criteria

0

1.00Pr

obab

ility

of a

ccep

ting

lot

Lot quality (fraction defective)

“Good” “Bad”

Ideal

Not verydiscriminating

Figure 10S.2

10S-9

Sampling TermsSampling 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 containing defectives exceeding the LTPD will be accepted

Producer’s risk: the probability that a lot containing the acceptable quality level will be rejected

10S-10

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

00.10.20.30.40.50.60.70.80.9

1

0 .05 .10 .15 .20 .25

Prob

abili

ty o

f acc

eptin

g lo

t

Lot quality (fraction defective)

= .10

= .10

“Good”

AQL

“Bad”Indifferent

LTPD

Figure 10S.3

10S-11

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

00.10.20.30.40.50.60.70.80.9

1

0 .10 .20 .30 .40 .50

Prob

abili

ty o

f acc

epta

nce

Fraction defective in lot

.9139

.7361

.5443

.3758

.2440.1493

.0860

10S-12

Average QualityAverage Quality Average outgoing quality (AOQ):

Average of inspected lots (100%) and uninspected lots

AOQ Pac p N nN

Pac = Probability of accepting lotp = Fraction defectiveN = Lot sizen = Sample size

10S-13

Example 10S-2: AOQExample 10S-2: AOQ

0 00.05 0.0460.1 0.074

0.15 0.0820.2 0.075

0.25 0.0610.3 0.045

0.35 0.030.4 0.019

00.010.020.030.040.050.060.070.080.09

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Approximate AOQL = .082

AO

Q (F

ract

ion

defe

ctiv

e ou

t)

Incoming fraction defective