Conestoga College

OPER 8025

CHAPTER S6

1)If a sample of items is taken and the mean of the sample is outside the control limits the process is

1. out of control and the cause should be established.
2. in control, but not capable of producing within the established control limits.
3. within the established control limits with only natural causes of variation.
4. monitored closely to see if the next sample mean will also fall outside the control limits.
5. producing high quality products.

2. The causes of variation in statistical process control are

1. cycles, trends, seasonality, and random variations.
2. producer's causes and consumer's causes.
3. mean and range.
4. natural causes and assignable causes.
5. Type I and Type II.

3. Natural variations

1. affect almost every production process.
2. are the many sources of variation that occur when a process is under control.

3. when grouped, form a pattern, or distribution.
4. are tolerated, within limits, when a process is under control.
5. All of the above are true.

4. Natural variations

1. are variations that are to be identified and investigated.
2. are variations that can be traced to a specific cause.
3. are the same as assignable variations.
4. lead to occasional false findings that processes are out of control.
5. play no role in statistical process control.

5. Assignable variation

1. is a sign that a process is under control.
2. is to be identified and investigated.
3. is the same as random variation.
4. is variation that cannot be traced to a specific cause.
5. leads to a steep OC curve.

6. Assignable causes

1. are not as important as natural causes.
2. are within the limits of a control chart.
3. depend on the inspector assigned to the job.
4. are also referred to as "chance" causes.
5. are causes of variation that can be identified and investigated.

7. Control charts for variables are based on data that come from

1. acceptance sampling.
2. individual items.
3. averages of small samples.
4. averages of large samples.
5. the entire lot.

8. The purpose of an x-bar chart is to determine whether there has been a

1. change in the dispersion of the process output.
2. change in the percent defective in a sample.
3. change in the central tendency of the process output.
4. change in the number of defects in a sample.
5. change in the AOQ.

9. The number of defects after a hotel room cleaning (sheets not straight, smears on mirror, missed debris on carpet, etc.) should be measured using a(n)

1. x-bar chart.
2. R-chart.
3. p-chart.
4. c-chart.
5. either x-bar or R chart.

10. The number of late insurance claim payouts per 100 should be measured with a(n)

1. x-bar chart.
2. R-chart.
3. p-chart.
4. c-chart.
5. either a p or c chart.

11. The upper and lower limits for diving ring diameters made by John's Swimming are 40 and 39 cm. John took 11 samples with the following average diameters (39, 39.1, 39.2, 39.3, 39.4,

39.5 39.6, 39.7, 39.8, 39.9, 40). Is the process in control?

1. Yes, no diameters exceeded the control limits.
2. No, some diameters exceeded the control limits.
3. No, there is a distinguishable pattern to the samples.
4. No, the range is not in control.
5. There is not enough information to make a decision.

12. Red Top Cab Company receives multiple complaints per day about driver behavior. Over 9 days the owner recorded the number of calls to be 3, 0, 8, 9, 6, 7, 4, 9, 8. What is the upper control limit for the c-chart?

A) 13.35

B) 8.45

C) 24.00

D) 0.00

E) 9.03

13. A process that is assumed to be in control with limits of 89 +/- 2 had sample averages of the following— 87.1, 87, 87.2, 89, 90, 89.5, 88.5, and 88. Is the process in control?

1. Yes.
2. No, one or more averages exceeded the limits.
3. Not enough information to tell.
4. No, there is a distinguishable trend.
5. No, two or more consecutive points are very near the lower (or upper) limit.

14. Which of the following is true about cutting costs at Canada Bankers Life Assurance Company?

1. They outsourced their call centre.
2. Customer satisfaction increased.
3. Customer service improved.
4. Quality metrics showed improvements.
5. Wastage decreased.

15. Ten samples of a process measuring the number of returns per 100 receipts were taken for a local retail store. The number of returns were 10, 9, 11, 7, 3, 12, 8, 4, 6, 11. Find the standard deviation of the sampling distribution. (Hint- Use p-bar formula)

A) There is not enough information.

B) .081

C) 8.1

D) .0273

E) .0863

16. An x-bar control chart was examined and no data points fell outside of the limits. Can this process be considered in control?

1. No, there could be a pattern to the points, the R-chart must be checked.
2. Yes, it is unlikely that there is a pattern in these points.
3. No, the number of samples must be known.
4. Yes.
5. Yes, there is not enough data to determine otherwise.

17. Statistical process control charts

1. display the measurements on every item being produced.
2. display upper and lower limits for process variables or attributes, and signal when a process is no longer in control.
3. indicate to the process operator the average outgoing quality of each lot.
4. indicate to the operator the true quality of material leaving the process.
5. display the measurements on every item being purchased.

18. Consumer's risk is the probability of

1. accepting a good lot.
2. rejecting a good lot.
3. rejecting a bad lot.
4. accepting a bad lot.
5. shipping a bad lot.

19. The Central Limit Theorem

1. is the theoretical foundation of the c-chart.
2. states that the average of assignable variations is zero.
3. allows managers to use the normal distribution as the basis for building some control charts.

4. states that the average range can be used as a proxy for the standard deviation.
5. controls the steepness of an operating characteristic curve.

20. For an x-bar chart where the standard deviation is known, the Upper Control Limit

1. is 3 . σ below the mean of sample means for a 3σ control chart.
2. is 3 . σ above the mean of sample means for a 3σ control chart.
3. is 3 . σ/ below the mean of sample means for a 3σ control chart.
4. is 3 . σ/ above the mean of sample means for a 3σ control chart.
5. Cannot be calculated unless the average range is known.

21. Up to three standard deviations above or below the centerline is the amount of variation that statistical process control allows for

1. Type I errors.
2. about 95.5% variation.
3. natural variation.
4. all types of variation.
5. assignable variation.

22. A manager wants to build 3-sigma control limits for a process. The target value for the mean of the process is 10 units, and the standard deviation of the process is 6. If samples of size 9 are to be taken, the UCL and LCL will be

1. -8 and 28.
2. 16 and 4.
3. 12 and 8.
4. 4 and 16.
5. 8 and 12.  

23. The type of inspection that classifies items as being either good or defective is

1. variable inspection.
2. attribute inspection.
3. fixed inspection.

4. all of the above.
5. none of the above.

24. The p-chart tells us whether there has been a

1. gain or loss in dispersion.

2. change in the percent defective in a sample.
3. change in the central tendency of the process output.
4. change in the number of defects in a sample.
5. none of the above.

25. The mean and standard deviation for a process for which we have a substantial history are μ

= 120 and σ = 2. For the x-bar chart, a sample size of 16 will be used. What is the mean of the sampling distribution?

A) 1/8 (0.125)

B) 7.5

3. 2
4. 40

E) 120

26. Jars of pickles are sampled and weighed. Sample measures are plotted on control charts. The ideal weight should be precisely 11 oz. Which type of chart(s) would you recommend?

1. p-charts
2. c-charts
3. - and R-charts
4. -, but not R-charts
5. both p- and c-charts

27. If = 23 ounces, σ = 0.4 ounces, and n = 16, the ±3σ control limits will be

1. 21.8 to 24.2 ounces.
2. 23 ounces.

C) 22.70 to 23.30 ounces.

D) 22.25 to 23.75 ounces.

E) 23.3 to 25.7 ounces.

28. The usual purpose of an R-chart is to signal whether there has been a

1. gain or loss in dispersion.
2. change in the percent defective in a sample.

3. change in the central tendency of the process output.
4. change in the number of defects in a sample.
5. change in sample size.

29. A manager wishes to build a 3-sigma range chart for a process. The sample size is five, the mean of sample means is 16.01, and the average range is 5.3. From Table S6.1 in the text, the appropriate value of is 0, and is 2.115. The UCL and LCL for this range chart are

A) 33.9 and 11.2.

B) 33.9 and 0.

C) 11.2 and 0.

D) 6.3 and 0.

E) 31.91 and 0.11.

30. Plots of sample ranges indicate that the most recent value is below the lower control limit. What course of action would you recommend?

1. Since there is no obvious pattern in the measurements, variability is in control.
2. One value outside the control limits is insufficient to warrant any action.
3. Lower than expected dispersion is a desirable condition; there is no reason to investigate.
4. The process is out of control; reject the last units produced.
5. Variation is not in control; investigate what created this condition.

31. To set -chart upper and lower control limits, one must know the process central line, which is the

1. average of the sample means.
2. total number of defects in the population.

3. percent defects in the population.
4. size of the population.
5. average range.

32. According to the text, the most common choice of limits for control charts is usually

1. ± 1 standard deviation.
2. ± 2 standard deviations.
3. ± 3 standard deviations.

4. ± 3 standard deviations for means and ± 2 standard deviations for ranges.
5. ± 1 standard deviations for means and ± 2 standard deviations for ranges.

33. Which of the following is true of a p-chart?

1. The lower control limit is found by subtracting a fraction from the average number of defects.
2. The lower control limit indicates the minimum acceptable number of defects.
3. The lower control limit equals D3 times p-bar.
4. The lower control limit may be at zero.
5. The lower control limit is the same as the lot tolerance percent defective.

34. The normal application of a p-chart is in

1. process sampling by variables.
2. acceptance sampling by variables.
3. process sampling by attributes.
4. acceptance sampling by attributes.
5. rejection sampling by attributes.

35. The statistical process chart used to control the number of defects per unit of output is the

1. -chart.
2. R-chart.
3. p-chart.
4. AOQ chart.
5. c-chart.

36. The c-chart signals whether there has been a

1. gain or loss in uniformity.
2. change in the number of defects per unit.
3. change in the central tendency of the process output.
4. change in the percent defective in a sample.
5. change in the AOQ.

37. The local newspaper receives several complaints per day about typographic errors. Over a seven-day period, the publisher has received calls from readers reporting the following number of errors: 4, 3, 2, 6, 7, 3, and 9. Based on these data alone, what type of control chart(s) should the publisher use?

1. p-chart
2. c-chart
3. -chart
4. R-chart
5. - and R-charts

38. A manufacturer uses statistical process control to control the quality of the firm's products. Samples of 50 of Product A are taken, and a defective/acceptable decision is made on each unit sampled. For Product B, the number of flaws per unit is counted. What type(s) of control charts should be used?

1. p-charts for A and B
2. p-chart for A, c-chart for B
3. c-charts for both A and B
4. p-chart for A, mean and range charts for B
5. c-chart for A, mean and range charts for B

39. A nationwide parcel delivery service keeps track of the number of late deliveries (more than 30 minutes past the time promised to clients) per day. They plan on using a control chart to plot

their results. Which type of control chart(s) would you recommend?

1. - and R-charts
2. p-charts
3. c-charts
4. -, but not R-charts
5. both p- and c-charts

40. A run test is used

1. to examine variability in acceptance sampling plans.
2. in acceptance sampling to establish control.
3. to examine points in a control chart to check for natural variability.
4. to examine points in a control chart to check for nonrandom variability.
5. in acceptance sampling to establish sample size.

41. The process capability measures Cp and Cpk differ because

1. only one ensures the process mean is centered within the limits.
2. Cp values above 1 indicate a capable process, Cpk values above 2 indicate a capable process.
3. both are identical.
4. Cp values for a given process will always be greater than or equal to Cpk values.
5. Cpk values for a given process will always be greater than Cp values.

42. A Cp of 1.33 indicates how many sigma limits?

A) 1

B) 1.33

3. 2
4. 3
5. 4  

43. Which of the following is true regarding the process capability index Cpk?

1. A Cpk index value of 1 is ideal, meaning all units meet specifications.
2. The larger the Cpk, the more units meet specifications.

3. The Cpk index can only be used when the process centerline is also the specification centerline.
4. Positive values of the Cpk index are good; negative values are bad.
5. The smaller the Cpk, the more units meet specifications.

44. If the Cpk index exceeds 1

1. the AQL must be smaller than the LTPD.
2. σ must be less than one-third of the absolute value of the difference between each specification and the process mean.
3. the x-bar chart must indicate that the process is in control.
4. the process is capable of Six Sigma quality.
5. the process is characterized as "not capable."

45. The statistical definition of Six Sigma allows for 3.4 defects per million. This is achieved by a Cpk index of

1. 0.
2. 1.

C) 1.33.

D) 1.67.

E) 2.  

46. A Cpk index of 1.00 equates to a defect rate of A) 5%.

2. 3.4 defects per million.
3. 2.7 per 1,000 items.

D) 97.23%.

E) 1%.

47. Acceptance sampling

1. is the application of statistical techniques to the control of processes.
2. was developed by Walter Shewhart of Bell Laboratories.

3. is used to determine whether to accept or reject a lot of material based on the evaluation of a sample.
4. separates the natural and assignable causes of variation.
5. is based on standard deviations rather than range values.

48. Acceptance sampling's primary purpose is to

1. estimate process quality.
2. identify processes that are out of control.
3. detect and eliminate defectives.
4. decide if a lot meets predetermined standards.
5. determine whether defective items found in sampling should be replaced.

49. An acceptance sampling plan's ability to discriminate between low quality lots and high quality lots is described by

1. a Gantt chart.
2. the Central Limit Theorem.
3. a process control chart.
4. an operating characteristics curve.
5. a range chart.

50. Acceptance sampling

1. may involve inspectors taking random samples (or batches) of finished products and measuring them against predetermined standards.
2. may involve inspectors taking random samples (or batches) of incoming raw materials and measuring them against predetermined standards.
3. is more economical than 100% inspection.
4. may be either of a variable or attribute type, although attribute inspection is more common in the business environment.
5. All of the above are true.

51. Which of the following statements on acceptance sampling is true?

1. Acceptance sampling draws samples from a population of items, tests the sample, and accepts the entire population if the sample is good enough, and rejects it if the sample is poor enough.
2. The sampling plan contains information about the sample size to be drawn and the critical acceptance or rejection numbers for that sample size.
3. The steeper an operating characteristic curve, the better its ability to discriminate between good and bad lots.
4. All of the above are true.
5. All of the above are false.

52. Acceptance sampling is usually used to control

1. the number of units output from one stage of a process which are then sent to the next stage.
2. the number of units delivered to the customer.
3. the quality of work-in-process inventory.
4. incoming lots of purchased products.
5. the number of outgoing units.

53. An operating characteristic (OC) curve describes

1. how many defects per unit are permitted before rejection occurs.
2. the sample size necessary to distinguish between good and bad lots.
3. the most appropriate sampling plan for a given incoming product quality level.
4. how well an acceptance sampling plan discriminates between good and bad lots.
5. how many defects per lot are permitted before rejection occurs.

54. An operating characteristics curve shows

1. upper and lower product specifications.
2. product quality under different manufacturing conditions.
3. how the probability of accepting a lot varies with the population percent defective.
4. when product specifications don't match process control limits.
5. how operations affect certain characteristics of a product.

55. Producer's risk is the probability of

1. accepting a good lot.
2. rejecting a good lot.
3. rejecting a bad lot.
4. accepting a bad lot.
5. overlooking defects.

56. Which of the following is true regarding the relationship between AOQ and the true population percent defective?

1. AOQ is greater than the true percent defective.
2. AOQ is the same as the true percent defective.
3. AOQ is less than the true percent defective.
4. There is no relationship between AOQ and the true percent defective.
5. The relationship between these two cannot be determined.

57. Average outgoing quality (AOQ) usually

1. worsens with inspection.
2. stays the same with inspection.
3. improves with inspection.
4. may either improve or worsen with inspection.
5. is the average quality before inspection.

58. A Type I error occurs when

1. a good lot is rejected.
2. a bad lot is accepted.
3. the number of defectives is very large.
4. the population is worse than the AQL.
5. a good lot is accepted.

59. A Type II error occurs when

1. a good lot is rejected.
2. a bad lot is accepted.

3. the population is worse than the LTPD.
4. the proportion of defectives is very small.
5. a good lot is accepted.

60. In most acceptance sampling plans, when a lot is rejected, the entire lot is inspected and all defective items are replaced. When using this technique the AOQ

1. worsens (AOQ becomes a larger fraction).
2. improves (AOQ becomes a smaller fraction).
3. is not affected, but the AQL is improved.
4. is not affected.
5. falls to zero.  

61. An acceptance sampling plan is to be designed to meet the organization's targets for product quality and risk levels. Which of the following is true?

1. n and c determine the AQL.
2. AQL, LTPD, α and β collectively determine n and c.
3. n and c are determined from the values of AQL and LTPD.
4. α and β are determined from the values of AQL and LTPD.
5. α and β determine the AQL.

62. When a lot has been accepted by acceptance sampling, we know that

1. it has more defects than existed before the sampling.
2. it has had all its defects removed by 100% inspection.
3. it will have the same defect percentage as the LTPD.
4. it has no defects present.
5. All of the above are false.

63. Which of the following statements about acceptance sampling is true?

1. The steeper an OC curve, the better it discriminates between good and bad lots.
2. Acceptance sampling removes all defective items.
3. Acceptance sampling of incoming lots is replacing statistical process control at the supplier.