Supplement
G Acceptance Sampling Plans
1. Acceptance Sampling Quality and Risk Decisions
• Acceptance Sampling: An inspection procedure used to determine whether to accept or reject
a specific quantity of materials (batch or “lot”). The consumer, sometimes in cooperation
with the producer, specifies the parameters of the acceptance sampling plan.
o Impact of TQM
• Basic procedure
o Take random sample.
o Accept or reject, based on results.
• Definitions:
o Producer, or seller, is origin of the material or service.
o Consumer, or buyer, is destination of the material or service.
o Sampling plan, a decision guide to control the risks of the producer (risk of rejecting
good-quality materials) and consumer (accepting bad-quality materials).
• Quality and risk decisions
o Acceptable quality level (AQL), a percentage of defects stated by the consumer in the
contract, and the aim of the producer. It is the quality level desired by the consumer
(emphasis added)
▪ Producer’s risk (
) is the probability that a shipment having exactly this level of
quality (the AQL) will be rejected when the lot is sampled using the specified
sampling plan.
Rejecting a good (AQL) lot is a type I error.
Consumers also desire low producer’s risk because sending good materials back
to the supplier disrupts the consumer’s production processes due to material
shortages, increases lead time, and creates poor supplier relations.
Most often the producer’s risk is set at 0.05, or 5 percent.
o Lot tolerance proportion defective (LTPD), the worst level the customer can tolerate.
The customer would not be happy, but probably wouldn’t sue.
▪ Consumer’s risk, (
) is the probability a shipment having exactly this level of
quality (the LTPD) will be accepted when the lot is sampled using the specified
sampling plan.
Accepting a bad (LTPD) lot is a type II error.
A common value for the consumer’s risk is 0.10, or 10 percent.
2. Sampling Plans
1. Single-sampling plans (for attributes)
• The plan states the sample size, n, and the acceptable number of defectives, c, found
in that sample.
• The accept-reject decision is based on the results of one sample.
• Single-sampling procedure for determining whether to accept a lot:
2. Double-sampling plan
• The double-sampling plan states two sample sizes, (
n1
and
n2
), and two acceptance
numbers (
c1
and
c2
).
• Double-sampling plans reduce costs of inspection for lots with very low or very high
proportion defective.
• Double-sampling procedure for determining whether to accept a lot:
Take a random sample of relatively small size n1, from a large lot.
Measure the quality characteristic to find the number of defectives in the original
sample.
If the sample passes the test (defects <
c1
), accept the lot.
If the sample fails (defects >
c2
), the entire lot is rejected.
If
c1
< defects <
c2
, then
Take a larger second random sample,
n2
; compare the total number of
defects found in both samples to
c2
.
If the combined number of defects <
c2
, accept the lot.
If the combined number of defects >
c2
, the entire lot is rejected.
3. Sequential-sampling plan
• A refinement of the double-sampling plan. Results of random samples, tested one-by-
one, are compared to sequential-sampling chart.
• Chart guides decision to reject, accept, or continue sampling, based on cumulative
results.
• Average number of items inspected (ANI) is generally lower with sequential sam–
pling.
3. Operating Characteristic Curves
• Perfect discrimination between good and bad lots requires 100% inspection.
• Select sample size n and acceptance number c to achieve the level of performance specified
by the AQL,
, LTPD, and
.
1. Drawing the OC curve (See Example G.1)
a. Each item inspected is either defective or not defective (binomial).
b. When n > 20 and p < 0.05, the Poisson distribution approximates the binomial
distribution. The Poisson distribution is used to prepare (OC) curves.
d. Drawing the OC Curve. Use Application G.1 to demonstrate the construction and use
of the OC curve.
A sampling plan is being evaluated where c = 10 and n = 193. If AQL = 0.03 and LTPD
= 0.08. What are the producer’s risk and consumer’s risk for the plan? Draw the OC
curve.
• Finding
(probability of rejecting AQL quality)
=
=
=
=
a
P
np
p
The short answers are: p = 0.03, np = 5.79, and Pa = 0.965. Therefore,
• Finding
(probability of accepting LTPD quality)
p
np
P
a
=
=
=
=
The short answers are:
e. Tutor G.1 in MyLab Operations Management provides a new example for constructing
an OC curve.
4. Selecting a Single-Sampling Plan
1. Sample size effect: increasing n while holding c constant increases the producer’s risk and
reduces the consumer’s risk
2. Acceptance level effect: increasing c while holding n constant decreases the producer’s risk
and increases the consumer’s risk
5. Average Outgoing Quality
• AOQ is the expected (or Average) proportion of defects that a particular sampling plan would
allow to pass through (Outgoing Quality from) inspection.
o Rectified inspection—defects found during the sampling process are removed and
reworked or replaced with conforming material.
o Rejected lots are subjected to 100% inspection.
o AOQL is the maximum value of the average outgoing quality over all possible values of
the proportion defective.
o Different sampling plans have different AOQs and AOQLs.
• The AOQL is found by calculating AOQ at several values for p, then setting AOQL equal to
the highest occurring AOQ. (See Example G.2.)
• Average Outgoing Quality. Use Application G.2 to demonstrate the model for computing
AOQ.
Management has selected the following parameters:
AQL
LTPD
n c
= =
= =
= =
001 005
006 010
100 3
. .
. .
What is the AOQ if p = 0.05 and N = 3000?
( )( )
==
=
=
=
3000
2900
AOQ
p
np
p
a
The short answers are:
• Tutor G.1 in MyLab Operations Management provides a new example for calculating the
AOQL.