Acceptance Sampling Plans

Transcription

1 Supplement I Supplement I Acceptance Sampling Plans Acceptance Sampling Plans TRUE/FALSE 1. Acceptance sampling is an inspection procedure used to determine whether to accept or reject a specific quantity of material. Answer: True Reference: Introduction Difficulty: Easy Keywords: acceptance, sampling, accept, reject 2. As more firms initiate total quality management systems, the need for acceptance sampling will increase. Answer: False Reference: Introduction Difficulty: Easy Keywords: acceptance, sampling 3. The lot tolerance proportion defective (LTPD) is the customer s desired level of quality. Answer: False Keywords: lot, tolerance, proportion, defective, LTPD 4. The chance that perfectly good material will be rejected based on a sample is known as a type I error. Answer: False Keywords: type I, alpha 5. A sequential sampling plan generally lowers the ANI. Answer: True Keywords: sequential, sampling, ANI, average, number, inspected 641

2 6. An operating characteristic curve is a plot of the probability of accepting the lot against the proportion defectives. Answer: True Reference: Operating Characteristic Curves Keywords: OC, operating, characteristic, probability, proportion 7. The distance between 1.0 and where the AQL intersects the OC curve is the value β (Beta). Answer: False Reference: Operating Characteristic Curves Keywords: OC, operating, characteristic, probability, Beta, AQL 8. Increasing c while holding n constant decreases the producer s risk and increases the consumer s risk. Answer: True Reference: Operating Characteristic Curves Keywords: OC, operating, characteristic, producer, consumer, risk 9. If the sample size is increased and the acceptance level is unchanged, the OC curve will have a higher consumer s risk. Answer: False Keywords: sample, size, acceptance, level, consumer s, risk, OC 10. 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. Answer: True Keywords: rectified, inspection MULTIPLE CHOICE 11. 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). Keywords: AQL, acceptable, quality, level 642

3 12. 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: c Keywords: type I, producer, risk, alpha 13. 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 laden with salmonella Answer: d Keywords: type II, consumer, risk, beta 14. Lot tolerance proportion defective (LTPD) can be defined as: a. the quality level desired by the consumer. b. the worst quality level the consumer can tolerate. c. the probability of rejecting a good lot (i.e., when a lot is, in fact, acceptable to the consumer). d. the probability of accepting a bad lot (i.e., when a lot is, in fact, not acceptable to the consumer). Answer: b Keywords: LTPD, lot, tolerance, percent, defective 15. 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. Answer: c Keywords: single, sampling, plan 643

4 16. A double-sampling plan has n 1 = 50, n 2 = 100, c 1 = 2, and c 2 = 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. Answer: c Keywords: double, sampling, plan 17. A double-sampling plan has n 1 = 50, n 2 = 100, c 1 = 2, and c 2 = 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. Keywords: double, sampling, plan 18. A double-sampling plan has n 1 = 50, n 2 = 100, c 1 = 2, and c 2 = 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. Answer: c Keywords: double, sampling, plan 19. 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: n 1, n 2, c 1, c 2. Keywords: sequential, sampling, plan 644

5 20. 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. Answer: c Difficulty: Hard Keywords: AQL, LTPD, acceptable, quality, level, lot, tolerance, percent, defective 21. 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. Difficulty: Hard Keywords: consumer, risk, sample, size 22. 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. Answer: b Difficulty: Hard Keywords: AQL, LTPD, acceptable, quality, level, lot, tolerance, percent, defective, consumer 23. 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. Difficulty: Hard Keywords: AQL, LTPD, acceptable, quality, level, lot, tolerance, percent, defective, producer 645

6 24. 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. Answer: b Difficulty: Hard Keywords: producer, risk, sample 25. 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. increases b. decreases c. increases d. and increase Difficulty: Hard Keywords: AQL, LTPD, acceptable, quality, level, lot, tolerance, percent, defective 26. 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. Answer: b Keywords: AOQ, quality, average, outgoing 27. 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 = Table I.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 Keywords: OC, sample, size, acceptance 646

7 28. A single-sampling plan by attributes is needed for a purchased component. Given the following information, what is the consumer s risk? Table I.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 Answer: d Keywords: consumer, risk 29. The quality manager has fixed n = 20 and c = 2 for a single-attribute sampling plan. Given AQL = 0.01 and LTPD = 0.05, what is the producer s risk? Table I.1 is appended to this exam. a. Between and 0.01 b. Between 0.01 and 0.1 c. Between 0.99 and d. Between 0.9 and 0.99 Keywords: producer, risk 30. A quality manager has established a sampling plan that calls for a sample size of 50 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.07. What is the producer s risk? Table I.1 is appended to this exam. a. Less than 0.07 b. Between 0.07 and 0.09 c. Between 0.09 and 0.11 d. Greater than 0.11 Answer: b Keywords: OC, operating, characteristic, producer, risk 647

8 31. A quality manager has established a sampling plan that calls for a sample size of 50 units and an acceptance number of 1 The supplier has agreed to a contract that calls for an AQL of 0.02 and an LTPD of.07. What is the consumer s risk? Table I.1 is appended to this exam. a. Less than 0.08 b. Between 0.08 and 0.10 c. Between 0.10 and 0.12 d. Greater than 0.12 Answer: d Keywords: OC, operating, characteristic, consumer, risk 32. A quality manager has established a sampling plan that calls for a sample size of 200 units and an acceptance number of 3. The supplier has agreed to a contract that calls for an AQL of 0.01 and an LTPD of.03. What is the producer s risk? Table I.1 is appended to this exam. a. More than 0.14 b. Between 0.14 and 0.12 c. Between 0.12 and 0.10 d. Less than 0.10 Keywords: OC, operating, characteristic, producer, risk 33. A quality manager has established a sampling plan that calls for a sample size of 200 units and an acceptance number of 3. The supplier has agreed to a contract that calls for an AQL of 0.01 and an LTPD of.03. What is the consumer s risk? Table I.1 is appended to this exam. a. Less than 0.14 b. Between 0.14 and 0.15 c. Between 0.15 and 0.16 d. Greater than 0.16 Answer: c Keywords: OC, operating, characteristic, consumer, risk 34. A quality manager has established a sampling plan that calls for a sample size of 100 units and an acceptance number of 2. The supplier has agreed to a contract that calls for an AQL of 0.01 and an LTPD of.05. Which of the following statements is TRUE? Table I.1 is appended to this exam. a. Lowering the acceptance number to 1 will raise the probability of a type II error. b. Increasing the sample size will increase α. c. Raising the AQL to 0.02 will lower the chance of a type I error. d. Reducing the LTPD to 0.04 will reduce the chance of a type II error. Answer: b Keywords: OC, operating, characteristic 648

9 35. 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 Which one of the following plans gives us the desired protection? Table I.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 Answer: b Keywords: AQL, LTPD, average, quality, level, lot, tolerance, percent, defective 36. Use Table I.1 for the following question. What is the acceptance number of a single-sampling plan if n = 400, AQL = 0.002, and = 0.01? a. c = 0 b. c = 1 c. c = 2 d. c = 3 Answer: d Keywords: acceptance, number 37. Use Table I.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 Answer: d Keywords: acceptance, number 38. A manufacturer wants a sampling plan in which AQL = 0.02, LPTD = 0.12, = 0.05, and = Which of the following values for n and c best satisfy these specifications? Table I.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 Keywords: sampling, plan, sample, size 649

10 39. 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 I.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 Answer: c Keywords: sample, size 40. 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. Table I.1 is appended to this exam. What is the value of? 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 Keywords: alpha, producer, risk 41. 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. Table I.1 is appended to this exam. What is the value of? 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 Answer: b Keywords: beta, consumer, risk 42. A lot of 2,000 items has just arrived. A single sampling calls for a sample size of 100 and c = 3. What is the average outgoing quality limit, assuming that all defectives in the entire lot are replaced if it is rejected and all defectives are replaced in the sample if it is accepted? Table I.1 is appended to this exam. a. Less than or equal to b. Greater than but less than or equal to c. Greater than but less than or equal to d. Greater than Answer: c Keywords: AQL, acceptable, quality, level 650

11 43. 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. Proportion Defective Probability of Acceptance What is the average outgoing quality limit for this plan? a. Less than or equal to b. Greater than but less than or equal to c. Greater than but less than or equal to d. Greater than Difficulty: Hard Keywords: AOQL, average, outgoing, quality, limit 44. A single-sampling plan has the following performance: Proportion Defective Probability of Acceptance 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 b. Greater than but less than or equal to c. Greater than but less than or equal to d. Greater than Answer: b Difficulty: Hard Keywords: AOQL, average, outgoing, quality, limit 651

12 45. A single-sampling plan using a sample size of 50 has the following performance: Proportion Defective Probability of Acceptance If the plan is used on a lot of 2,000 items, what is the average outgoing quality limit? a. Less than or equal to b. Greater than but less than or equal to c. Greater than but less than or equal to d. Greater than Answer: c Difficulty: Hard Keywords: AOQL, average, outgoing, quality, limit 46. The average outgoing quality (AOQ) is: a. the proportion of defectives that the sampling plan will allow to pass. b. the proportion of non-defectives that the sampling plan will allow to pass. c. the highest proportion of defectives that the sampling plan will allow to pass. d. the lowest proportion of defectives that the sampling plan will allow to pass. Difficulty: Easy Keywords: AOQ, average, outgoing, quality 47. 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. Answer: b Difficulty: Easy Keywords: AOQ, average, outgoing, quality 652

13 48. A single-sampling plan using a sample size of 50 on a lot size of 2,000 has the following performance: Proportion Defective Probability of Acceptance 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. Answer: d Keywords: AOQL, average, outgoing, quality, limit 653

14 49. This OC curve represents a sampling plan developed for a lot size of 1000, 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? Probability of Acceptance P a. Less than b. Greater than or equal to but less than c. Greater than or equal to but less than d. Greater than or equal to Answer: c Keywords: AOQL, average, outgoing, quality, limit 654

15 50. 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? Probability of Acceptance P a. Less than b. Greater than or equal to 0.06 but less than c. Greater than or equal to 0.07 but less than d. Greater than or equal to Answer: d Keywords: AOQL, average, outgoing, quality, limit 655

16 51. This OC curve represents a sampling plan developed for a lot size of 1000, 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? Probability of Acceptance P a b c d Answer: b Difficulty: Hard Keywords: AOQL, average, outgoing, quality, limit 656

17 52. 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? Probability of Acceptance P a. Less than b. Greater than or equal to 0.08 but less than c. Greater than or equal to 0.09 but less than d. Greater than or equal to Answer: b Keywords: AOQL, average, outgoing, quality, limit 657

18 53. 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? p Pa 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. Answer: c Difficulty: Hard Keywords: AOQL, average, outgoing, quality, limit, lot, size FILL-IN-THE-BLANK 54. is an inspection procedure used to determine whether to accept or reject a specific quantity of material. Answer: Acceptance sampling Reference: Introduction Difficulty: Easy Keywords: acceptance, sampling 658

19 55. is the quality level desired by the consumer. Answer: Acceptable quality level, AQL Keywords: AQL, acceptable, quality, level 56. is the risk that the sampling plan will fail to verify an acceptable lot s quality and thus reject it a type I error. Answer: Producer s risk, Keywords: producer, risk, type I 57. is the worst level of quality that the customer can tolerate. Answer: Lot tolerance proportion defective, LTPD Keywords: LTPD, lot, tolerance, percent, defective 58. is the risk that a lot with LTPD will be accepted a type II error. Answer: Consumer s risk, Keywords: consumer, risk, beta, type II, LTPD 59. A double-sampling plan has a lower than a single-sampling plan. Answer: ANI, average number of items inspected Keywords: ANI, average, number, items, inspected 60. A(n) is when the consumer randomly selects items from the lot and inspects them one by one. Answer: sequential-sampling plan s Keywords: sequential, sampling, plan 61. Increasing c while holding n constant decreases the risk and increases the risk. Answer: producer s, consumer s Keywords: producer, consumer, risk 659

20 62. Replacing all defective items in a rejected lot and all defective items in a sample with good items is called inspection. Answer: rectified Keywords: rectified, inspection 63. The maximum value of the average outgoing quality over all possible values of the proportion defective is called the. verage outgoing quality limit, AOQL Keywords: AOQL, average, outgoing, quality, limit 64. A small can be disregarded in AOQ calculations involving an extremely large lot size. Answer: samples size (n) Keywords: AOQ, average, outgoing, quality, lot, sample, size SHORT ANSWERS 65. Discuss the two incorrect conclusions that can be made when using acceptance sampling. Answer: 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. Keywords: producer, consumer 66. If you were interested in minimizing the average number of items inspected, which sampling plan would you choose? Why? Answer: The sequential sampling plan minimizes the average number of items inspected because with each item inspected, there is a chance that a decision can be made to accept or reject the lot. Keywords: ANI, average, number, inspected 67. Why is an operating-characteristic (OC) curve useful? Answer: OC curves describe how well a sampling plan discriminates between good and bad lots. It shows the probability of accepting a lot for each proportion defective in a specified range. s Keywords: OC, operating, characteristic 660

21 68. Relative to an acceptance sampling plan, what is the net effect of increasing n while holding c constant? Answer: The producer s risk will increase and the consumer s risk will decrease. s Keywords: n, c, OC, operating, characteristic, sample 69. The AOQ is often lower for a supplier with a high fraction defective than for a supplier with a comparatively lower fraction defective. Why wouldn t a supplier with a lower fraction defective always have a better AOQ? Answer: Average outgoing quality is based on the probability of accepting a lot with a certain fraction defective, given a sample (and lot) size. If a supplier has a very small fraction defective, it is unlikely that the inspection sample contains any defectives, so the lot will be accepted. A supplier with a much higher fraction defective will produce lots that trigger 100% inspection, resulting in more defective product being weeded out and a better AOQ. Keywords: AOQ, average, outgoing, quality 661

22 PROBLEMS 70. A single-sampling plan by attributes is needed for a purchased component. Table I.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: a. What is the producer s risk,? b. What is the consumer s risk,? c. Draw the OC curve for this plan. Answer: a. =.080 b. =.238 c. Probability of p acceptance Reference: Multiple sections Keywords: OC, operating, characteristics, producer, consumer, risk 662

23 71. This OC curve represents a single sampling plan conducted on a lot size of 200 with a sample size of 20 and an acceptance number of 1. The y-coordinates of the first few points have been labeled; the x coordinates appear on the x-axis. If the receiving company uses rectified inspection, what is the greatest fraction defective that will enter their production process? Answer: Average outgoing quality is calculated as the product of the OC curve XY coordinates adjusted by the sample and lot sizes. The first few points in the graph are: ppa ( N n) AOQ N (200 20) AOQ (200 20) AOQ AOQL (200 20) AOQ (200 20) AOQ The largest value ( ) is the AOQL, which is the greatest fraction defective that will enter the receiving company s product stream. Keywords: OC, operating, characteristics, AQL, AOQL, average, outgoing, quality, limit 663

24 TABLE I.1 Producer s Risk Consumer s Risk n (p = AQL) (p = LTPD)