Operations Management: Processes and Supply Chains, 12e (Krajewski)
Supplement G Acceptance Sampling Plans
1) Acceptance sampling is an inspection procedure used to determine whether to accept or reject a
specific quantity of material.
2) As more firms initiate total quality management systems, the need for acceptance sampling will
increase.
3) The lot tolerance proportion defective (LTPD) is the customer’s desired level of quality.
4) Acceptable quality level can be defined as the:
A) quality level desired by the consumer.
B) worst quality level the consumer can tolerate.
C) probability of rejecting a good lot (i.e., when a lot is, in fact, acceptable to the consumer).
D) probability of accepting a bad lot (i.e., when a lot is, in fact, not acceptable to the consumer).
5) Which of the following is an example of a type I error?
A) buying a carton of eggs at the store and discovering that one was broken
B) releasing a guilty defendant
C) returning your computer for warranty repair when the fault was caused by user error
D) passing defective materials from a supplier into your processes to keep your workers busy
6) Which of the following is an example of a type II error?
A) convicting an innocent defendant
B) returning your “dead” stereo for warranty repair when its malfunction was caused by it not being
plugged in
C) halting production to adjust a machine when your process was actually in control
D) eating food that has spoiled
7) Lot tolerance proportion defective (LTPD) can be defined as the:
A) quality level desired by the consumer.
B) worst quality level the consumer can tolerate.
C) probability of rejecting a good lot (i.e., when a lot is, in fact, acceptable to the consumer).
D) probability of accepting a bad lot (i.e., when a lot is, in fact, not acceptable to the consumer).
8) ________ is an inspection procedure used to determine whether to accept or reject a specific quantity of
material.
9) ________ is the quality level desired by the consumer.
10) ________ is the risk that the sampling plan will fail to verify an acceptable lot’s quality and thus reject
it—a type I error.
11) ________ is the worst level of quality that the customer can tolerate.
12) ________ is the risk that a lot with LTPD will be accepted—a type II error.
13) Discuss the two incorrect conclusions that can be made when using acceptance sampling.
14) What is the basic idea of incoming inspection? Why does a producer perform it?
15) Discuss producer’s risk and consumer’s risk.
Answer: Producer‘s risk is the chance that good product is rejected and consumer’s risk is the chance that
bad product is accepted. Although producers are interested in low risk, they often have no control over
G.2 Sampling Plans
1) A double-sampling plan requires two sample sizes and two acceptance numbers.
2) A double-sampling plan is usually less expensive than a single-sampling plan if the lot has a high
number of defectives.
3) A double-sampling plan is usually less expensive than a single-sampling plan if the lot has a low
number of defectives.
4) A sequential sampling plan generally lowers the ANI.
5) A single-sampling plan has n = 200 and c = 6. A sample is taken and five items are found to be
defective. What should be done?
A) Another sample should be taken.
B) The lot should be rejected.
C) The lot should be accepted.
D) The five items should be repaired, and then the entire lot should be accepted.
6) A double-sampling plan has n1 = 50, n2 = 100, c1 = 2, and c2 = 4. Suppose on the first sample, one
defective item was discovered. What should be done?
A) Reject the entire lot.
B) Take a second sample of 100 units.
C) Accept the entire lot.
D) Repair the defective units, and accept the entire lot.
7) A double-sampling plan has n1 = 50, n2 = 100, c1 = 2, and c2 = 4. Suppose on the first sample, five
defectives were discovered. How many total items will be inspected before a decision is reached?
A) 50
B) 100
C) 150
D) This cannot be determined with the information provided.
8) A double-sampling plan has n1 = 50, n2 = 100, c1 = 2, and c2 = 4. Suppose the first sample revealed two
defectives. What should be done?
A) Reject the entire lot.
B) Take a second sampling of 100 units.
C) Accept the entire lot.
D) Repeat the tests on the first sample.
9) Which of the following statements is true?
A) Sequential-sampling plans are preferred to single-sampling plans because the average number of
items inspected is generally lower.
B) With a sequential-sampling plan, each time an item is inspected, a decision is made to accept or reject a
lot.
C) With a sequential-sampling plan, sampling continues until the lot is rejected.
D) Sequential-sampling plans are defined by four parameters: n1, n2, c1, c2.
10) A double-sampling plan has a lower ________ than a single-sampling plan.
11) In general, a sequential sampling strategy will require a lower number of items be inspected if the
actual percentage of defectives in the lot is ________.
12) A(n) ________ is when the consumer randomly selects items from the lot and inspects them one by
one.
13) If you were interested in minimizing the average number of items inspected, which type of sampling
plan would you choose? Why?
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14) Describe the process of a single-sampling plan.
15) Describe the process of a double-sampling plan.
Answer: In a double-sampling plan, management specifies two sample sizes (n1 and n2) and two
acceptance numbers (c1 and c2). If the quality of the lot is very good or very bad, the consumer can make
a decision to accept or reject the lot on the basis of the first sample, which is smaller than in the single–
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G.3 Operating Characteristic Curves
1) An operating characteristic curve is a plot of the probability of accepting the lot against the proportion
defectives.
2) The distance between 1.0 and where the AQL intersects the OC curve is the value β (Beta).
3) Increasing c while holding n constant decreases the producer’s risk and increases the consumer’s risk.
4) For a given AQL and LTPD, which one of the following statements about the single-sampling plan is
true?
A) If c stays constant but n is increased, both the producer’s risk and the consumer’s risk will increase.
B) If c stays constant but n is increased, both the producer’s risk and the consumer’s risk will decrease.
C) If n stays constant but c is increased, the producer’s risk will decrease and the consumer’s risk will
increase.
D) If n stays constant but c is increased, the producer’s risk will increase and the consumer’s risk will
decrease.
5) Which one of the following will increase the consumer’s risk?
A) Decrease sample size and hold constant the number of defective items in a sample.
B) Decrease the acceptable number of defective items in a sample and hold constant the sample size.
C) Increase the sample size and decrease the acceptable number of defective items in a sample.
D) Decrease the acceptable quality level and hold constant both sample size and the acceptable number of
defective items in a sample.
6) Which one of the following alternatives will reduce the consumer‘s risk for a given AQL and LTPD?
A) Reduce n and keep c constant.
B) Increase n and keep c constant.
C) Reduce n and increase c.
D) Increase beta.
7) Which one of the following alternatives will reduce the producer‘s risk for a given AQL and LTPD?
A) Reduce n and keep c constant.
B) Increase n and keep c constant.
C) Increase n and reduce c.
D) Increase alpha.
8) Which one of the following actions will decrease the producer‘s risk?
A) Increase n and keep c constant.
B) Decrease n and keep c constant.
C) Keep n constant and decrease c.
D) Increase n and decrease c.
9) The management of a company wishes to develop a new acceptance sampling plan that keeps
acceptable quality level, lot tolerance proportion defective, and c constant. If the sample size (n) is
increased, compared to the prior plan, which of the following is true?
A) α increases
B) α decreases
C) β increases
D) α and β increase
10) The average outgoing quality (AOQ) is:
A) the average number of good units produced per hour.
B) the expected proportion of defects a sampling plan will allow.
C) the level of quality desired by the customer.
D) the worst level of quality tolerated by the consumer.
11) An item is purchased with one surface polished to a specified finish quality. From each incoming
shipment, a sample of items is randomly selected and the polished surface of each sample item is
compared with a standard and judged to be either acceptable or unacceptable. The following parameters
have been established: AQL = 0.02, = 0.05, LTPD = 0.09, and = 0.10. Table G.1 is appended to this exam.
What are the sample size and the acceptance number?
A) n = 89, c = 4
B) n = 39, c = 1
C) n = 43, c = 1
D) n = 237, c = 15
12) A company wants to develop an acceptance sampling plan that keeps the producer’s risk at 0.03 or
less and the customer’s risk at 0.10 or less. The acceptable quality level (AQL) is 0.01, and the lot tolerance
proportion defective (LTPD) has been set at 0.10. Which one of the following plans gives us the desired
protection? Table G.1 is appended to this exam.
A) c = 3, n = 190
B) c = 2, n = 54
C) c = 1, n = 30
D) c = 1, n = 20
13) Use Table G.1 for the following question. What is the acceptance number of a single-sampling plan if
n = 400, AQL = 0.002, and α= 0.01?
A) c = 0
B) c = 1
C) c = 2
D) c = 3
14) Use Table G.1 for the following question. What is the acceptance number of a single-sampling plan if
n = 300, LPTD = 0.02, and = 0.15?
A) c = 0
B) c = 1
C) c = 2
D) c = 3
15) A manufacturer wants a sampling plan in which AQL = 0.02, LPTD = 0.12, α = 0.05, and β = 0.10.
Which of the following values for n and c best satisfy these specifications? Table G.1 is appended to this
exam.
A) n = 54, c = 3
B) n = 100, c = 2
C) n = 200, c = 1
D) n = 162, c = 0
16) A company is developing an acceptance sampling plan to monitor quality. The acceptable quality
level (AQL) is 0.01, and a sampling plan having c = 5 is being considered. If a producer’s risk of 0.03 is
desired, what should be the sample size? Table G.1 is appended to this exam.
A) less than or equal to 25
B) more than 25 but less than or equal to 175
C) more than 175 but less than or equal to 325
D) more than 325
17) An ideal OC curve is shaped like a ________.
18) A graph that demonstrates how well a sampling plan distinguishes between shipments that should be
accepted and shipments that should be rejected is a(n) ________.
19) Why is an operating-characteristic (OC) curve useful?
20) Relative to an acceptance sampling plan, what is the net effect of increasing n while holding c
constant?
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21) A single-sampling plan by attributes is needed for a purchased component. Table G.1 is appended to
this exam.
Sample size = 80
Acceptance number (c) = 1
Acceptance quality level (AQL) = 0.02
Lot tolerance proportion defective (LTPD) = 0.06
Given the preceding information, draw the OC curve for this plan.
Answer:
Pct
Defective
Pac
AOQ
0.00
1.0000
0.0000
0.01
0.8092
0.0081
0.02
0.5230
0.0105
0.03
0.3038
0.0091
0.04
0.1654
0.0066
0.05
0.0861
0.0043
0.06
0.0433
0.0026
0.07
0.0211
0.0015
0.08
0.0101
0.0008
0.09
0.0047
0.0004
0.10
0.0022
0.0002
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G.4 Selecting a Single-Sampling Plan
1) If the sample size is increased and the acceptance level is unchanged, the OC curve will have a higher
consumer‘s risk.
2) If the sample size is increased and the acceptance level is unchanged, the OC curve will have a slope
that is more negative.
3) A single-sampling plan by attributes is needed for a purchased component. Given the following
information, what is the consumer’s risk? Table G.1 is appended to this exam.
Sample size = 50
Acceptance number (c) = 3
Acceptance quality level (AQL) = 0.01
Lot tolerance proportion defective (LTPD) = 0.04
A) greater than or equal to 0 but less than or equal to 0.25
B) greater than 0.25 but less than or equal to 0.50
C) greater than 0.50 but less than or equal to 0.75
D) greater than 0.75 but less than or equal to 1.00
4) A single-sampling plan by attributes is needed for a purchased component. Given the following
information, what is the producer’s risk? Table G.1 is appended to this exam.
Sample size = 75
Acceptance number (c) = 2
Acceptance quality level (AQL) = 0.01
Lot tolerance proportion defective (LTPD) = 0.04
A) .01
B) .02
C) .03
D) .04
5) A single-sampling plan by attributes is needed for a purchased component. Given the following
information, what is the producer’s risk? Table G.1 is appended to this exam.
Sample size = 75
Acceptance number (c) = 3
Acceptance quality level (AQL) = 0.01
Lot tolerance proportion defective (LTPD) = 0.04
A) .007
B) .008
C) .009
D) .010