Acceptance Sampling

Supplement 10

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10S-2

You should be able to:LO 10S.1 Explain the purpose of acceptance

samplingLO 10S.2 Compare and contrast single- and

multiple-sampling plansLO 10S.3 Describe what an operating

characteristic curve doesLO 10S.4 Determine the average outgoing

quality of inspected lots

Supplement 10: Learning Objectives

10S-3

Acceptance samplingA form of inspection applied to lots or batches

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

May be applied to both attribute and variable inspection

Acceptance Sampling

LO 10S.1

10S-4

Purpose of Acceptance SamplingThe purpose of acceptance sampling is to

decide whether a lot satisfies predetermined standardsLots that satisfy these standards are passed or

acceptedRejected lots may be subjected to 100 percent

inspectionIn the case of purchased goods, they may be

returned for credit or replacement

LO 10S.1

10S-5

Single-Sampling PlanSingle-sampling plan

One random sample is drawn from each lotEvery item in the sample is inspected and

classified as “good” or “defective”If any sample contains more than a specified

number of defectives, c, the lot is rejected

LO 10S.2

10S-6

Double-Sampling Plan Allows the opportunity to take a second sample if the results of

the initial sample are inconclusiveTwo values are specified for the number of defective items

A lower level, c1

An upper level, c2 If the number of defectives in the first sample is

≤ c1 the lot is accepted and sampling is terminated > c2 the lot is rejected and sampling is terminated Between c1 and c2 a second sample is collected

The number of defectives in both samples is compared to a third value, c3 If the combined number of defectives does not exceed this value,

the lot is accepted; otherwise, it is rejected

Double-Sampling Plan

LO 10S.2

10S-7

Multiple-sampling plan Similar to a double-sampling plan except more than two

samples may be required A sampling plan will specify each sample size and two limits for

each sampleThe limit values increase with the number of samples If, for any sample, the cumulative number of defectives

found exceeds the upper limit specified, the lot is rejected If for any sample the cumulative number of defectives found

is less than or equal to the lower limit, the lot is accepted. If the number of defectives found is between the two limits,

another sample is takenThe process continues until the lot is accepted or rejected

Multiple-Sampling Plan

LO 10S.2

10S-8

Operating Characteristic (OC) CurveAn important sampling plan characteristic is

how it discriminates between high and low quality

OC curves describe a sampling plan’s ability to discriminate OC curve

Probability curve that shows the probabilities of accepting lots with various fractions defective

LO 10S.3

10S-9

OC Curve

A typical OC Curve for Proportions

LO 10S.3

10S-10

Acceptable Defect LevelsAcceptable quality Level (AQL)

The percentage level 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

LO 10S.3

10S-11

An OC Curve

The AQL indicates good lots, and the LTPD indicates bad lots

LO 10S.3

10S-12

An interesting feature of acceptance sampling is that the level of inspection automatically adjusts to the quality of the lots being inspected, assuming rejected lots are subjected to 100 percent inspectionGood lots have a high probability and bad lots a

low probability of being accepted.If the lots inspected are mostly good, few will end

up going through 100 percent inspection.The poorer the quality of the lots, the greater the

number of lots that will come under close scrutiny

Average Quality of Inspected Lots

LO 10S.4

10S-13

Average outgoing qualityAverage of rejected lots (100 percent

inspection) and accepted lots (a sample of items inspected)

Average Outgoing Quality

size Sample defectiveFraction

sizeLot lot theaccepting ofy Probabilit

where

AOQ

np

NP

N

nNpP

ac

ac

LO 10S.4

10S-14

In practice, the last term of the AOQ formula is close to 1.0

Eliminate this term, so

Construct the AOQ curve for this situationN = 500, n = 10, and c = 1

AOQ

pPacAOQ

p .05 .10 .15 .20 .25 .30 .35 .40

pac .9193

.7361

.5443

.3758

.2440

.0860

.0860

.0464

AOQ .046

.074

.082

.075

.061

.045

.030

.019

LO 10S.4

10S-15

0

0.02

0.04

0.06

0.08

0.1

0 0.1 0.2 0.3 0.4 0.5

AO

Q

Incoming fraction defective

AOQ Curve

Approximate AOQ = .082

LO 10S.4