Deck 24: Supplement G Acceptance Sampling Plans

Question 1

Discuss the two incorrect conclusions that can be made when using acceptance sampling.

Answer 1

The two incorrect conclusions are to reject a lot of good product and to accept a lot of defective product. The chance of rejecting a lot of good product is called the producer's risk or a type I error, and is usually set at 5 percent. The chance of accepting a defective lot is called consumer's risk or a type II error, and is usually set at 10 percent.

Question 2

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

Answer 2

C

Question 3

________ is an inspection procedure used to determine whether to accept or reject a specific quantity of material.

Answer 3

Acceptance sampling

Question 4

A double-sampling plan is usually less expensive than a single-sampling plan if the lot has a high number of defectives.

Question 5

________ is the worst level of quality that the customer can tolerate.

Question 6

________ is the quality level desired by the consumer.

Question 7

Acceptance sampling is an inspection procedure used to determine whether to accept or reject a specific quantity of material.

Question 8

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

Question 9

A double-sampling plan is usually less expensive than a single-sampling plan if the lot has a low number of defectives.

Question 10

A double-sampling plan requires two sample sizes and two acceptance numbers.

Question 11

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).

Question 12

What is the basic idea of incoming inspection? Why does a producer perform it?

Question 13

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).

Question 14

________ is the risk that the sampling plan will fail to verify an acceptable lot's quality and thus reject it-a type I error.

Question 15

The lot tolerance proportion defective (LTPD) is the customer's desired level of quality.

Question 16

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.

Question 17

________ is the risk that a lot with LTPD will be accepted-a type II error.

Question 18

As more firms initiate total quality management systems, the need for acceptance sampling will increase.

Question 19

A sequential sampling plan generally lowers the ANI.

Question 20

Discuss producer's risk and consumer's risk.

Question 21

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.

Question 22

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 ________.

Question 23

The distance between 1.0 and where the AQL intersects the OC curve is the value β (Beta).

Question 24

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.

Question 25

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.

Question 26

A double-sampling plan has a lower ________ than a single-sampling plan.

Question 27

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

Question 28

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.

Question 29

Describe the process of a single-sampling plan.

Question 30

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.

Question 31

Describe the process of a double-sampling plan.

Question 32

If you were interested in minimizing the average number of items inspected, which type of sampling plan would you choose? Why?

Question 33

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.

Question 34

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.

Question 35

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.

Question 36

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.

Question 37

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.

Question 38

Increasing c while holding n constant decreases the producer's risk and increases the consumer's risk.

Question 39

A(n) ________ is when the consumer randomly selects items from the lot and inspects them one by one.

Question 40

An operating characteristic curve is a plot of the probability of accepting the lot against the proportion defectives.

Question 41

Why is an operating-characteristic (OC) curve useful?

Question 42

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

Question 43

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

Question 44

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

Question 45

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

Question 46

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

Question 47

If the sample size is increased and the acceptance level is unchanged, the OC curve will have a higher consumer's risk.

Question 48

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.

Question 49

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

Question 50

If the sample size is increased and the acceptance level is unchanged, the OC curve will have a slope that is more negative.

Question 51

An ideal OC curve is shaped like a ________.

Question 52

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) ________.

Question 53

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 = 75
Acceptance number (c) = 2
Acceptance quality level (AQL) = 0.01
Lot tolerance proportion defective (LTPD) = 0.05

A) )25
B) )27
C) )29
D) )31

Question 54

Relative to an acceptance sampling plan, what is the net effect of increasing n while holding c constant?

Question 55

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 = 100
Acceptance number (c) = 1
Acceptance quality level (AQL) = 0.01
Lot tolerance proportion defective (LTPD) = 0.05

A) )028
B) )033
C) )037
D) )041

Question 56

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 = 100
Acceptance number (c) = 1
Acceptance quality level (AQL) = 0.02
Lot tolerance proportion defective (LTPD) = 0.07

A) )003
B) )004
C) )005
D) )006

Question 57

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 = 75
Acceptance number (c) = 3
Acceptance quality level (AQL) = 0.01
Lot tolerance proportion defective (LTPD) = 0.05

A) )46
B) )48
C) )50
D) )52

Question 58

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

Question 59

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

Question 60

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

Question 61

This OC curve represents a sampling plan developed for a lot size of 1,000, a sample size of 15, and an acceptance number of 2. The probability of acceptance for each of the first six points appears next to the plotted point. What is the average outgoing quality for an incoming fraction defective of 0.25?

A) less than 0.045
B) greater than or equal to 0.045 but less than 0.055
C) greater than or equal to 0.055 but less than 0.065
D) greater than or equal to 0.065

Question 62

This OC curve represents a sampling plan developed for a lot size of 1,000, a sample size of 15, and an acceptance number of 2. The probability of acceptance for each of the first six points appears next to the plotted point. What incoming fraction defective is associated with the average outgoing quality limit?

A) 0.10
B) 0.15
C) 0.20
D) 0.25

Question 63

Champion Cooling Company has developed a sampling plan calling for a sample size of 25 and an acceptance number of 1. The proportion defective and probability of acceptance appear in the table. Floyd Electric, their supplier ships whatever Champion Cooling asks; sometimes the lot size is as small as 30 units and it has been as large as 10,000 units. Champion Cooling decides to stick with what they know, a sample size of 25 and an acceptance number of 1 despite advice to the contrary. Which statement regarding their sampling plan is best?

A) The average outgoing quality level will remain constant since the sample size and the acceptance number do not change.
B) The average outgoing quality level will vary as the lot size varies, but the average outgoing quality limit will remain constant.
C) The incoming fraction defective that produces the average outgoing quality limit will remain the same regardless of lot size.
D) The incoming fraction defective that produces the average outgoing quality limit will vary as the lot size varies.

Question 64

A quality manager has established a sampling plan that calls for a sample size of 75 units and an acceptance number of 2. The supplier has agreed to a contract that calls for an AQL of 0.02 and an LTPD of .04. What is the AOQL? Table G.1 is appended to this exam.

A) less than 0.11
B) between 0.11 and 0.14
C) between 0.14 and 0.17
D) greater than 0.17

Question 65

A sample of 100 items is randomly selected from a shipment of incoming materials. AQL and LTPD have been established at 0.01 and 0.07, respectively. When four or more defective items are found in a sample, the shipment is rejected. What is the value of α? Table G.1 is appended to this exam.

A) less than or equal to 0.04
B) greater than 0.04 but less than or equal to 0.06
C) greater than 0.06 but less than or equal to 0.08
D) greater than 0.08

Question 66

This OC curve represents a sampling plan developed for a lot size of 500, a sample size of 15, and an acceptance number of 2. The probability of acceptance for each of the first six points appears next to the plotted point. What is the average outgoing quality for an incoming fraction defective of 0.15?

A) less than 0.06
B) greater than or equal to 0.06 but less than 0.07
C) greater than or equal to 0.07 but less than 0.08
D) greater than or equal to 0.08

Question 67

A quality manager has established a sampling plan that calls for a sample size of 75 units from a shipment of 5,000 pieces and an acceptance number of 2. The supplier has agreed to a contract that calls for an AQL of 0.02 and an LTPD of .04. What is the AOQ if the actual percentage of defectives in the lot is 2%? Table G.1 is appended to this exam.

A) less than 0.014
B) between 0.014 and 0.018
C) between 0.018 and 0.022
D) greater than 0.022

Question 68

This OC curve represents a sampling plan developed for a lot size of 500, a sample size of 15, and an acceptance number of 2. The probability of acceptance for each of the first six points appears next to the plotted point. What is the average outgoing quality limit?

A) less than 0.08
B) greater than or equal to 0.08 but less than 0.09
C) greater than or equal to 0.09 but less than 0.10
D) greater than or equal to 0.10

Question 69

The AOQL is the highest point in the plot of AOQ over all possible values of the proportion defective.

Question 70

A single-sampling plan using a sample size of 50 on a lot size of 2,000 has the following performance:
Today the company making the purchase receives two lots of 2,000 items and the inspection department is in a big hurry. Which action will result in an identical AOQL for the purchasing company?

A) Take a random sample of 25 from each lot and accept or reject both lots based on the results.
B) Take a random sample of 50 from one lot and accept or reject the second lot based on the first lot's results.
C) Take a random sample of 100 from one lot and accept or reject the second lot based on the first lot's results.
D) Take a random sample of 50 from each lot and accept or reject each lot based on the results.

Question 71

A sample of 100 items is randomly selected from a shipment of incoming materials. AQL and LTPD have been established at 0.01 and 0.07, respectively. When four or more defective items are found in a sample, the shipment is rejected. What is the value of β? Table G.1 is appended to this exam.

A) less than or equal to 0.05
B) greater than 0.05 but less than or equal to 0.10
C) greater than 0.10 but less than or equal to 0.15
D) greater than 0.15

Question 72

Increasing c while holding n constant decreases the ________ risk and increases the ________ risk.

Question 73

Rectified inspection occurs when all defective items in the lot are replaced with good items if the lot is rejected and any defective items in the samples are replaced if the lot is accepted.

Question 74

A single-sampling plan has the following performance:
What is the average outgoing quality limit if the sample size is 200 and the lot size is 6,000?

A) less than or equal to 0.0200
B) greater than 0.0200 but less than or equal to 0.0220
C) greater than 0.0220 but less than or equal to 0.0230
D) greater than 0.0230

Question 75

A rectified inspection plan requires that:

A) a rejected lot be returned to the supplier.
B) a rejected lot be subjected to 100% inspection.
C) a sample with too many defectives be returned to the lot for mixing and resampling.
D) all units in the sample be returned to the lot if it is rejected.

Question 76

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 = 125
Acceptance number (c) = 4
Acceptance quality level (AQL) = 0.02
Lot tolerance proportion defective (LTPD) = 0.07

A) )06
B) )11
C) )16
D) )21

Question 77

A lot of 1,000 items is on the loading dock. A single-sampling plan calls for a sample size of 10. The following table gives the probability of acceptance for the plan over a range of possible quality levels.
What is the average outgoing quality limit for this plan?

A) less than or equal to 0.018
B) greater than 0.0180 but less than or equal to 0.0200
C) greater than 0.0200 but less than or equal to 0.0220
D) greater than 0.0220

Question 78

The average outgoing quality (AOQ) is the:

A) proportion of defectives that the sampling plan will allow to pass.
B) proportion of non-defectives that the sampling plan will allow to pass.
C) highest proportion of defectives that the sampling plan will allow to pass.
D) lowest proportion of defectives that the sampling plan will allow to pass.

Question 79

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 = 125
Acceptance number (c) = 4
Acceptance quality level (AQL) = 0.02
Lot tolerance proportion defective (LTPD) = 0.07

A) )057
B) )061
C) )065
D) )069

Question 80

A single-sampling plan by attributes is needed for a purchased component. Table G.1 is appended to this exam.
Sample size = 100
Acceptance number (c) = 2
Acceptance quality level (AQL) = 0.01
Lot tolerance proportion defective (LTPD) = 0.04
Given the preceding information: