Chapter 10S – Acceptance Sampling
10S-1
CHAPTER 10S
ACCEPTANCE SAMPLING
Teaching Notes
Accounting may be particularly appreciative of this segment on acceptance sampling because it
involves exactly the same principles as auditing.
There are three points in the production process where monitoring takes place: before production,
during production, and after production. The logic of checking conformance before production is to
make sure that inputs are acceptable. The logic of checking conformance during production is to make
sure that the conversion of inputs into outputs is proceeding in an acceptable manner. The logic of
checking conformance of output is to make a final verification of conformance before passing goods
on to customers.
Monitoring before and after production involves acceptance sampling procedures; monitoring during
the production process is referred to as process control. These procedures are explained in detail in the
following pages. For both acceptance sampling and process control, inspection provides key data for
decision making.
Answers to Discussion and Review Questions
1. The objective of acceptance sampling is to make a decision on whether to accept or reject a
lot. It is not to estimate lot quality.
2. Process control involves monitoring quality during the production process. Acceptance
3. An operating characteristic curve is the relationship between lot quality and probability of lot
4. The two basic factors in choosing between single and multiple-sampling are the cost per
sample and the cost per observation. Single sampling is characterized by one sample of many
5. a. AOQ is the average quality of outgoing lots as a function of the fraction defective.
Outgoing lots include rejected lots (subjected to 100% inspection after being rejected) and
accepted lots.
b. AOQL is the maximum average outgoing quality (AOQ) for a given acceptance sampling
plan.
c. LTPD is the lot tolerance percent defective, and refers to the upper limit on the percentage
of defects that a consumer is willing to accept.
Chapter 10S – Acceptance Sampling
10S-2
d. The alpha risk refers to the producer’s risk or a Type I error: the probability that a good lot
will be rejected on the basis of sample data.
e. A beta risk refers to the consumer’s risk, or a Type II error: the probability that a bad lot
will be accepted on the basis of sample data.
Solutions:
1. Given:
Inspection cost during trigger assembly = $12/hr. Replacement cost at final assembly = $30
per defective. Inspection rate = one trigger per minute.
Determine inspection cost per piece:
hr
./12$
b. Indifference point (percent defective) between 100% inspection and only final inspection
(with replacement):
Let x = percent defective:
Cost of inspecting a piece = $.20/piece
Cost of replacement at final assembly = $30/piece (x)
Chapter 10S – Acceptance Sampling
2. Given:
Samples of n = 20 are tested in each lot of 4,000 received. Lots with more than one defective
are pulled and subjected to 100% inspection.
a. OC curve:
Given:
N = 4,000
n = 20
c = 1
Use the binomial distribution table from Appendix B because n/N = 20/4,000 = .005 < .05.
p
Pac
.05
.7358
10
.3917
.15
.1756
.20
.0692
.25
.0243
.30
.0076
.35
.0021
.40
.0005
OC Curve
1.00
.90
.80
.70
.60
.50
Pac
Chapter 10S – Acceptance Sampling
10S-4
b. Approximate AOQL:
p
Pac
p(Pac)
.05
.7358
.037
.10
.3917
.039
.15
.1756
.026
.20
.0692
.014
.25
.0243
.006
.30
.0076
.002
.35
.0021
.001
.40
.0005
.000
fraction defective
.05 .10 .15 .20 .25 .30
AOQ Curve
AOQL .039
.05
.04
.03
AOQ
Chapter 10S – Acceptance Sampling
3. Given:
If any defects are found, 100% inspection is used.
a. Given:
N = 8,000
OC curve
1.00
.80
.60
.40
Pac
Chapter 10S – Acceptance Sampling
b. Given:
N = 8,000
n = 150
c = 0
Use the Poisson distribution table from Appendix B because n > 20 & p < .05 as
shown in the table below.
p
μ = np
Pac
p(Pac)
.001
.15
.861
.009
.002
.30
.741
.0015
.003
.45
.638
.0019
.004
.60
.549
.0022
.005
.75
.472
.0024
.006
.90
.407
.0024
.008
1.20
.301
.0024
.010
1.50
.223
.0022
.012
1.80
.165
.0020
OC Curve
Pac
1.00
.80
.60
.40