jee maths exam for nov-om

Chapter 10 - Quality Control

Chapter 10Quality Control

True / False Questions

1. Approving the effort that occurs during the production process is known as acceptance sampling. True False

2. Statistical Process Control is the measurement of rejects in the final product. True False

3. The optimum level of inspection occurs when we catch at least 98.6 percent of the defects. True False

4. The optimum level of inspection minimizes the sum of inspection costs and the cost of passing defectives. True False

5. Processes that are in control eliminate variations. True False

6. High-cost, low-volume items often require careful inspection since we make them so infrequently. True False

7. Low-cost, high-volume items often require more intensive inspection. True False

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8. A lower control limit must by definition be a value less than an upper control limit. True False

9. Attributes need to be measured, variable data can be counted. True False

10. The amount of inspection we choose can range from no inspection at all to inspecting each item numerous times. True False

11. The amount of inspection needed is governed by the costs of inspection and the expected costs of passing defective items. True False

12. The purpose of statistical process control is to ensure that historical output is random. True False

13. A process that exhibits random variability would be judged to be out of control. True False

14. If a point on a control chart falls outside one of the control limits, this suggests that the process output is non-random and should be investigated. True False

15. An x-bar control chart can only be valid if the underlying population it measures is a normal distribution. True False

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16. Concluding a process is out of control when it is not is known as a Type I error. True False

17. An R value of zero (on a range chart) means that the process must be in control since all sample values are equal. True False

18. Range charts are used mainly with attribute data. True False

19. Range charts and p-charts are both used for variable data. True False

20. A p-chart is used to monitor the fraction of defectives in the output of a process. True False

21. A c-chart is used to monitor the total number of defectives in the output of a process. True False

22. A c-chart is used to monitor the number of defects per unit for process output. True False

23. Tolerances represent the control limits we use on the charts. True False

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24. "Process capability" compares "process variability" to the "tolerances." True False

25. Control limits used on process control charts are specifications established by design or customers. True False

26. Control limits tend to be wider for more variable processes. True False

27. Patterns of data on a control chart suggest that the process may have non-random variation. True False

28. The output of a process may not conform to specifications even though the process may be statistically "in control." True False

29. Run tests are useful in helping to identify nonrandom variations in a process. True False

30. Run tests give managers an alternative to control charts; they are quicker and cost less. True False

31. Statistical process control focuses on the acceptability of process output. True False

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32. A run test checks a sequence of observations for randomness. True False

33. Even if the process is not centered, the process capability index (indicated by Cpk) is very useful. True False

34. The process capability index (indicated by Cpk) can be used only when the process is centered. True False

35. Quality control is assuring that processes are performing in an acceptable manner. True False

36. The primary purpose of statistical process control is to detect a defective product before it is shipped to a customer. True False

37. The Taguchi Cost Function suggests that the capability ratio can be improved by extending the spread between LCL and UCL. True False

38. The variation of a sampling distribution is tighter than the variation of the underlying process distribution. True False

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39. The sampling distribution can be assumed to be approximately normal even when the underlying process distribution is not normally distributed. True False

40. Approximately 99.7% of sample means will fall within ± two standard deviations of the process mean if the process is under control. True False

41. The best way to assure quality is to use extensive inspection and control charts. True False

42. Control limits are based on multiples of the process standard deviation. True False

43. Attribute data are counted, variable data are measured. True False

44. The number of defective parts in a sample is an example of variable data because it will "vary" from one sample to another. True False

45. Larger samples will require wider x-bar control limits because there is more data. True False

46. When a process is not centered, its capability is measured in a slightly different way. The symbol for this case is Cpk. True False

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47. Range control charts are used to monitor process central tendency. True False

48. An "up and down" run test uses the median as a reference point and measures the percentage above and below the median. True False

49. "Assignable variation" is variation due to a specific cause, such as tool wear. True False

50. Variation in a sample statistic collected from a process may be either random variation or assignable variation - or both. True False

51. "Quality of conformance" is concerned with whether a product or service conforms to its specifications. True False

52. The larger the process variation, the tighter the specifications should be. True False

53. Type I and Type II errors refer to the magnitude of variation from the standard. True False

54. The greater the capability ratio, the higher the rejects. True False

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55. Non-random variation is likely whenever all observations are between the LCL and UCL. True False

Multiple Choice Questions

56. Which of the following quality control sample statistics indicates a quality characteristic that is an attribute? A. meanB. varianceC. standard deviationD. rangeE. proportion

57. A time-ordered plot of representative sample statistics is called a: A. Gantt chartB. SIMO-chartC. Control ChartD. Up-Down MatrixE. Standard deviation table

58. A control chart used to monitor the process mean is the: A. p-chartB. R-chartC. x-bar chartD. c-chartE. Gantt chart

59. A control chart used to monitor the fraction of defectives generated by a process is the: A. p-chartB. R-chartC. x-bar chartD. c-chartE. Gantt chart

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60. A p-chart would be used to monitor _______. A. average shrinkageB. dispersion in sample dataC. the fraction defectiveD. the number of defects per unitE. the range of values

61. A c-chart is used for: A. meansB. rangesC. percent defectiveD. fraction defective per unitE. number of defects per unit

62. A control chart used to monitor the number of defects per unit is the: A. p-chartB. R-chartC. x-bar chartD. c-chartE. Gantt chart

63. A point which is outside of the lower control limit on an R-chart: A. is an indication that no cause of variation is presentB. should be ignored because it signifies better than average qualityC. should be investigated because an assignable cause of variation might be presentD. should be ignored unless another point is outside that limitE. is impossible since the lower limit is always zero

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64. If a process is performing as it should, it is still possible to obtain observations which are outside of which limits?(I) tolerances(II) control limits(III) process variability A. IB. IIC. I and IID. II and IIIE. I, II, and III

65. Which of the following relationships must always be incorrect? A. Tolerances > process variability > control limitsB. Process variability > tolerances > control limitsC. Tolerances > control limits > process variabilityD. Process variability > control limits > tolerancesE. Process variability <Tolerances<control limits

66. Which of the following is not a step in the quality control process? A. define what is to be controlledB. compare measurements to a standardC. eliminate each of the defects as they are identifiedD. take corrective action if necessaryE. evaluate corrective action

67. The probability of concluding that assignable variation exists when only random variation is present is:(I) the probability of a Type I error(II) known as the alpha risk(III) highly unlikely (IV) the sum of probabilities in the two tails of the normal distribution A. I and IIB. I and IVC. II and IIID. I, II, and IVE. I, III, and IV

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68. _______ variation is a variation whose cause can be identified. A. AssignableB. ControllableC. RandomD. StatisticalE. Theoretical

69. A plot below the lower control limit on the range chart:(I) should be ignored since lower variation is desirable(II) may be an indication that process variation has decreased(III) should be investigated for assignable cause A. I and IIB. I and IIIC. II and IIID. II onlyE. I, II, and III

70. A shift in the process mean for a measured characteristic would most likely be detected by a: A. p-chartB. x-bar chartC. c-chartD. R-chartE. s-chart

71. The range chart (R-chart) is most likely to detect a change in: A. proportionB. meanC. number defectiveD. variabilityE. sample size

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72. The optimum level of inspection is where the: A. cost of inspection is minimumB. cost of passing defectives is minimumC. total cost of inspection and defectives is maximumD. total cost of inspection and defectives is minimumE. difference between inspection and defectives costs is minimum

73. The purpose of control charts is to: A. estimate the proportion of output that is acceptableB. weed out defective itemsC. determine if the output is within tolerances/specificationsD. distinguish between random variation and assignable variation in the processE. provide meaningful work for quality inspectors

74. The process capability index (Cpk) may mislead if:(I) the process is not stable.(II) the process output is not normally distributed.(III) the process is not centered. A. I and IIB. I and IIIC. II and IIID. II onlyE. I, II and III

75. A time-ordered plot of sample statistics is called a(n) ______ chart. A. StatisticalB. InspectionC. ControlD. SIMOE. Limit

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Essay Questions

76. A process that makes chocolate candy bars has an output that is normally distributed with a mean of 6 oz. and a standard deviation of .01 oz. A job is to be run that requires 200 candy bars. Determine three sigma control limits for an x-bar chart assuming a sample size of 10.If specifications are 5.98 to 6.02, what run size should be used for this job so that the expected number of good candy bars is 200, assuming the process is in control?

77. Four samples of three observations each have been taken, with actual measurements (in centimeters) shown below. Construct three-sigma mean and range charts.

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78. A town's department of public works is concerned about adverse public reaction to a sewer project that is currently in progress. Because of this, the Commissioner of Public Works has authorized a weekly survey to be conducted of town residents. Each week, a sample of 100 residents is questioned on their feelings towards the project. The results to date are shown below. Analyze this data using control charts that would provide for a 5% risk of Type I error.

79. Construct the appropriate two-sigma control chart for the sample observations listed below.

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80. Perform run tests on the given data. What can you conclude?

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81. The chart below depicts 16 sample means that were taken at periodic intervals and plotted on a control chart. Does the output appear to be random?

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82. Given the following control chart, would you say that the process appears to be performing appropriately?

83. An analyst has gathered data and counted the number of runs with respect to the median. There were 60 observations and 22 runs. What can the analyst conclude given this information?

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84. An operator collected the following time series data from a process:

(A) Determine the number of A/B runs.(B) Determine the number of up/down runs.

85. An analyst counted 17 A/B runs and 15 U/D runs in 26 time series observations. Do these results suggest that the data are non-random?


86. The number of runs up and down for the data above is: A. 3B. 4C. 5D. 6E. none of these

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87. The number of runs with respect to the sample median is: A. 3B. 4C. 5D. 6E. none of these

The following data occurs chronologically from left to right:


89. The number of runs up and down is: A. 2B. 3C. 4D. 5E. none of these

A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results:

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90. What is the sample mean service life for sample 2? A. 460 hoursB. 495 hoursC. 500 hoursD. 515 hoursE. 525 hours

91. What is the mean of the sampling distribution of sample means when service life is in control? A. 250 hoursB. 470 hoursC. 495 hoursD. 500 hoursE. 515 hours

92. What is the standard deviation of the sampling distribution of sample means for whenever service life is in control? A. 5 hoursB. 6.67 hoursC. 10 hoursD. 11.55 hoursE. 20 hours

93. If he uses upper and lower control limits of 520 and 480 hours, what is his risk (alpha) of concluding service life is out of control when it is actually under control (Type I error)? A. 0.0026B. 0.0456C. 0.3174D. 0.6826E. 0.9544

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94. If he uses upper and lower control limits of 520 and 480 hours, on what sample(s) (if any) does service life appear to be out of control? A. sample 1B. sample 2C. sample 3D. both samples 2 and 3E. all samples are in control

A Quality Analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that whenever this process is under control, package weight is normally distributed with a mean of twenty ounces and a standard deviation of two ounces. Each day last week, he randomly selected four packages and weighed each:

95. What is the sample mean package weight for Thursday? A. 19 ouncesB. 20 ouncesC. 20.6 ouncesD. 21 ouncesE. 23 ounces

96. What is the mean of the sampling distribution of sample means when this process is under control? A. 18 ouncesB. 19 ouncesC. 20 ouncesD. 21 ouncesE. 22 ounces

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97. What is the standard deviation of the sampling distribution of sample means for whenever this process is under control? A. 0.1 ouncesB. 0.4 ouncesC. 0.5 ouncesD. 1 ounceE. 2 ounces

98. If he uses upper and lower control limits of 22 and 18 ounces, what is his risk (alpha) of concluding this process is out of control when it is actually in control (Type I error)? A. 0.0026B. 0.0456C. 0.3174D. 0.6826E. 0.9544

99. If he uses upper and lower control limits of 22 and 18 ounces, on what day(s), if any, does this process appear to be out of control? A. MondayB. TuesdayC. Monday and TuesdayD. Monday, Tuesday, and ThursdayE. none

A Quality Analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results:

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100. What is the sample mean for machine #1? A. 15B. 16C. 17D. 21E. 23

101. What is the estimate of the process mean for whenever it is under control? A. 16B. 19C. 20D. 21E. 23

102. What is the estimate of the sample average range based upon this limited sample? A. 13.0B. 4.33C. 5.4D. 4.2E. 2.0

103. What are the x-bar chart three sigma upper and lower control limits? A. 22 and 18B. 23.29 and 16.71C. 23.5 and 16.5D. 23.16 and 16.84E. 24 and 16

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104. For upper and lower control limits of 23.29 and 16.71, which machine(s), if any, appear(s) to have an out-of-control process mean? A. machine #1B. machine #2C. machine #3D. all of the machinesE. none of the machines

The Chair of the Operations Management Department at Quality University wants to construct a p-chart for determining whether the four faculty teaching the basic P/OM course are under control with regard to the number of students who fail the course. Accordingly, he sampled 100 final grades from last year for each instructor, with the following results:

105. What is the sample proportion of failures (p) for Prof. D? A. 0B. .04C. .11D. .13E. .16

106. What is the estimate of the mean proportion of failures for these instructors? A. .10B. .11C. .13D. .16E. .40

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107. What is the estimate of the standard deviation of the sampling distribution for an instructor's sample proportion of failures? A. .0075B. .03C. .075D. .3E. .75

108. What are the .95 (5% risk of Type I error) upper and lower control limits for the p-chart? A. .95 and .05B. .13 and .07C. .1588 and .0412D. .16 and .04E. .1774 and .0226

109. Using .95 control limits, (5% risk of Type I error), which instructor(s), if any, should he conclude is (are) out of control? A. noneB. Prof. BC. Prof. DD. both Prof. B and Prof. DE. all

A Quality Analyst wants to construct a control chart for determining whether four machines, all producing the same product, are under control with regard to a particular quality attribute. Accordingly, she inspected 1,000 units of output from each machine in random samples, with the following results:

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110. What is the sample proportion of defectives for machine #1? A. .023B. .02C. .0115D. .0058E. .005

111. What is the estimate of the process proportion of defectives for whenever it is under control? A. .08B. .06C. .04D. .02E. .01

112. What is the estimate of the standard deviation of the sampling distribution of sample proportions for whenever this process is under control? A. .016B. .00016C. .04D. .0044E. .00002

113. What are the control chart upper and lower control limits for an alpha risk of .05? A. .0272 and .0128B. .0287 and .0113C. .029 and .013D. .0303 and .0097E. .0332 and .0068

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114. For upper and lower control limits of .026 and .014, which machine(s), if any, appear(s) to be out-of-control for process proportion of defectives? A. machine #3B. machine #4C. machines #3 and #4D. machines #2 and #3E. none of the machines

Essay Questions

Given the following process control data for a normally distributed quality variable (three samples of size four each):

115. What is the sample mean for sample #1? #2? #3?

116. If the process is known to have a mean of 15 and a standard deviation of 3, what is the mean of the sampling distribution of sample means for whenever this process is under control? The standard deviation?

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117. If the process is known to have a mean of 15 and a standard deviation of 3, what is the alpha risk (probability of Type I error) for upper and lower control limits of 16.5 and 13.5 respectively? 18 and 12? 19.5 and 10.5?

118. If the process is known to have a mean of 15 and a standard deviation of 3, what are the three sigma upper and lower control limits for an x-bar chart?

119. If the process is known to have a mean of 15 and a standard deviation of 3, using three sigma control limits, do any of the sample means indicate an out-of-control process mean?

Given the following process control data for a quality attribute (three samples of size 400 each):

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120. What is the sample proportion of defectives for sample #1? #2? #3?

121. If the process is known to produce 11 percent defectives on average, what is the mean of the sampling distribution of sample proportions for whenever this process is under control? The standard deviation?

122. If the process is known to produce 11 percent defectives on average, what is the alpha risk (probability of Type I error) for upper and lower control limits of .1256 and .0944 respectively? .1412 and .0788? .1568 and .0632?

123. If the process is known to produce 11 percent defectives on average, what are the upper and lower control limits for an alpha risk of .10? .05? .01?

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124. If the process is known to produce 11 percent defectives on average, using three sigma control limits, do any of the sample proportions indicate an out-of-control process proportion of defectives?

125. If the process proportion of defectives is unknown, what is the estimate of it?

126. If the process proportion of defectives is unknown, what is the alpha risk (probability of Type I error) for upper and lower control limits of .115 and .085 respectively? .13 and .07? .145 and .055?

127. If the process proportion of defectives is unknown, what are the upper and lower control limits for an alpha risk of .10? .05? .01?

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128. If the process proportion of defectives is unknown, using .10 alpha risk control limits, do any of the sample proportions indicate an out-of-control process proportion of defectives?

A stint for use is coronary surgery requires a special coating. Specifications for this coating call for it to be at least 0.05 millimeters but no more than 0.15 millimeters.

129. If, when the coating process is in control, the long-run average is 0.09 millimeters, what metric would be used to assess this process' capability?

130. Suppose the long-run average of this coating process is 0.09 millimeters. Further suppose this process' standard deviation is 0.015 millimeters. What proportion of the output from this process will fail to meet specifications?

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131. Suppose the criterion for evaluating this process is that the appropriate capability index must be at least 1.3. With a long-run process mean of 0.09 and a standard deviation of 0.015, is this process capable?

132. Assuming that the process mean of 0.09 cannot be changed, what process standard deviation would be required for this process to be considered capable (assuming that a capable process must have a capability index of at least 1.3)?


133. Studies on a bottle-filling machine indicates it fills bottles to a mean of 16 ounces with a standard deviation of 0.10 ounces. What is the process specification, assuming the Cpk index of 1? A. 0.10 ouncesB. 0.20 ouncesC. 0.30 ouncesD. 16.0 ounces plus or minus 0.30 ouncesE. none of the above

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134. Studies on a machine that molds plastic water pipe indicate that when it is injecting 1-inch diameter pipe, the process standard deviation is 0.05 inches. The one-inch pipe has a specification of 1-inch plus or minus 0.10 inch. What is the process capability index (Cpk) if the long-run process mean is 1 inch? A. 0.50B. 0.67C. 1.00D. 2.00E. none of the above

135. The specification limit for a product is 8 cm and 10 cm. A process that produces the product has a mean of 9.5 cm and a standard deviation of 0.2 cm. What is the process capability, Cpk? A. 3.33B. 1.67C. 0.83D. 2.50E. none of the above

136. The specifications for a product are 6 mm ± 0.1 mm. The process is known to operate at a mean of 6.05 with a standard deviation of 0.01 mm. What is the Cpk for this process? A. 3.33B. 1.67C. 5.00D. 2.50E. none of the above

137. Organizations should work to improve process capability so that quality control efforts can become more ________. A. effectiveB. efficientC. necessaryD. unnecessaryE. widespread

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138. A process results in a few defects occurring in each unit of output. Long-run, these defects should be monitored with ___________. A. p-chartsB. c-chartsC. x-bar chartsD. r-chartsE. o-charts

139. When a process is in control, it results in there being, on average, 16 defects per unit of output. C-chart limits of 8 and 24 would lead to a _______ chance of a Type I error. A. 67%B. 92%C. 33%D. .03%E. 5%

140. When a process is in control, it results in there being, on average, 16 defects per unit of output. C-chart limits of 4 and 28 would lead to a _______ chance of a Type I error. A. 67%B. 92%C. 33%D. 0.3%E. 5%

141. The basis for a statistical process control chart is a(the) __________. A. process capabilityB. sampling distributionC. control limitD. sample rangeE. sample mean

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Chapter 10 Quality Control Answer Key

True / False Questions

1. Approving the effort that occurs during the production process is known as acceptance sampling. FALSE

Acceptance sampling occurs before or after the production process.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: MediumLearning Objective: 10-01 List and briefly explain the elements of the control process.Topic Area: Inspection

2. Statistical Process Control is the measurement of rejects in the final product. FALSE

SPC is the evaluation of the process.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: MediumLearning Objective: 10-01 List and briefly explain the elements of the control process.Topic Area: Statistical Process Control

3. The optimum level of inspection occurs when we catch at least 98.6 percent of the defects. FALSE

The optimum level of inspection is when the sum of inspection costs and the cost of passing defectives are equal.

AACSB: Reflective ThinkingBloom's: UnderstandDifficulty: MediumLearning Objective: 10-01 List and briefly explain the elements of the control process.Topic Area: Inspection

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4. The optimum level of inspection minimizes the sum of inspection costs and the cost of passing defectives. TRUE

This represents the optimum balance between inspection and failure costs.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: EasyLearning Objective: 10-01 List and briefly explain the elements of the control process.Topic Area: Inspection

5. Processes that are in control eliminate variations. FALSE

In control, processes are free of non-random variation.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: MediumLearning Objective: 10-02 Explain how control charts are used to monitor a process; and the concepts that underlie their use.Topic Area: Statistical Process Control

6. High-cost, low-volume items often require careful inspection since we make them so infrequently. TRUE

These are good candidates for inspection.


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7. Low-cost, high-volume items often require more intensive inspection. FALSE

These are not good candidates for inspection.

AACSB: Reflective ThinkingBloom's: UnderstandDifficulty: MediumLearning Objective: 10-01 List and briefly explain the elements of the control process.Topic Area: Inspection

8. A lower control limit must by definition be a value less than an upper control limit. TRUE

The lower limit must be smaller than the upper limit.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: EasyLearning Objective: 10-02 Explain how control charts are used to monitor a process; and the concepts that underlie their use.Topic Area: Statistical Process Control

9. Attributes need to be measured, variable data can be counted. FALSE

Attributes need to be counted, variable data is measured.


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10. The amount of inspection we choose can range from no inspection at all to inspecting each item numerous times. TRUE

These are the extremes of inspection.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: EasyLearning Objective: 10-01 List and briefly explain the elements of the control process.Topic Area: Inspection

11. The amount of inspection needed is governed by the costs of inspection and the expected costs of passing defective items. TRUE

These interact to set the optimum amount of inspection.

AACSB: Reflective ThinkingBloom's: UnderstandDifficulty: EasyLearning Objective: 10-01 List and briefly explain the elements of the control process.Topic Area: Inspection

12. The purpose of statistical process control is to ensure that historical output is random. FALSE

It is to ensure that non-random variation is detected and corrected.

AACSB: Reflective ThinkingBloom's: UnderstandDifficulty: MediumLearning Objective: 10-02 Explain how control charts are used to monitor a process; and the concepts that underlie their use.Topic Area: Statistical Process Control

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13. A process that exhibits random variability would be judged to be out of control. FALSE

All processes exhibit random variability.


14. If a point on a control chart falls outside one of the control limits, this suggests that the process output is non-random and should be investigated. TRUE

A point outside the control limits suggests non-random variation.


15. An x-bar control chart can only be valid if the underlying population it measures is a normal distribution. FALSE

The sample average typically is normally distributed regardless of the underlying distribution of the process.

AACSB: Reflective ThinkingBloom's: UnderstandDifficulty: HardLearning Objective: 10-02 Explain how control charts are used to monitor a process; and the concepts that underlie their use.Topic Area: Statistical Process Control

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16. Concluding a process is out of control when it is not is known as a Type I error. TRUE

A Type I error involves erroneously concluding that a process is out of control.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: HardLearning Objective: 10-02 Explain how control charts are used to monitor a process; and the concepts that underlie their use.Topic Area: Statistical Process Control

17. An R value of zero (on a range chart) means that the process must be in control since all sample values are equal. FALSE

If the sample size is sufficiently large, an R of zero could indicate an out of control process.


18. Range charts are used mainly with attribute data. FALSE

Range charts are used with variable data.


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19. Range charts and p-charts are both used for variable data. FALSE

P-charts are used with attribute data.


20. A p-chart is used to monitor the fraction of defectives in the output of a process. TRUE

P-charts involve the fraction of defectives.


21. A c-chart is used to monitor the total number of defectives in the output of a process. FALSE

A c-chart is used to monitor the number of defects per unit, not defective units.

AACSB: Reflective ThinkingBloom's: UnderstandDifficulty: HardLearning Objective: 10-02 Explain how control charts are used to monitor a process; and the concepts that underlie their use.Topic Area: Statistical Process Control

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22. A c-chart is used to monitor the number of defects per unit for process output. TRUE

A c-chart monitors the number of defects per unit for process output.


23. Tolerances represent the control limits we use on the charts. FALSE

Tolerances are specification limits, not control limits.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: HardLearning Objective: 10-05 Assess process capability.Topic Area: Process Capability

24. "Process capability" compares "process variability" to the "tolerances." TRUE

Process variability influences how much output falls outside of tolerances.


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25. Control limits used on process control charts are specifications established by design or customers. FALSE

Control limits are independent of specifications.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: MediumLearning Objective: 10-05 Assess process capability.Topic Area: Statistical Process Control

26. Control limits tend to be wider for more variable processes. TRUE

Process with inherently more variability will naturally have wider control limits.


27. Patterns of data on a control chart suggest that the process may have non-random variation. TRUE

Ideally, the data on a control chart will have no pattern.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control

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28. The output of a process may not conform to specifications even though the process may be statistically "in control." TRUE

A process can be free of non-random variation and still not meet specifications.

AACSB: Reflective ThinkingBloom's: UnderstandDifficulty: HardLearning Objective: 10-05 Assess process capability.Topic Area: Process Capability

29. Run tests are useful in helping to identify nonrandom variations in a process. TRUE

Runs tests are useful to identify non-randomness in patterns.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: MediumLearning Objective: 10-04 Perform run tests to check for nonrandomness in process output.Topic Area: Statistical Process Control

30. Run tests give managers an alternative to control charts; they are quicker and cost less. FALSE

Runs tests are not alternatives to control charts.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: EasyLearning Objective: 10-04 Perform run tests to check for nonrandomness in process output.Topic Area: Statistical Process Control

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31. Statistical process control focuses on the acceptability of process output. FALSE

Statistical process control focuses on the variability of processes.


32. A run test checks a sequence of observations for randomness. TRUE

Runs tests can be used to detect nonrandomness in sequences of observations.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: MediumLearning Objective: 10-04 Perform run tests to check for nonrandomness in process output.Topic Area: Statistical Process Control

33. Even if the process is not centered, the process capability index (indicated by Cpk) is very useful. FALSE

If the process is not centered, Cpk is not useful.

AACSB: Reflective ThinkingBloom's: UnderstandDifficulty: MediumLearning Objective: 10-05 Assess process capability.Topic Area: Process Capability

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34. The process capability index (indicated by Cpk) can be used only when the process is centered. FALSE

Cpk can be used whether or not the process is centered.

AACSB: Reflective ThinkingBloom's: UnderstandDifficulty: MediumLearning Objective: 10-05 Assess process capability.Topic Area: Process Capability

35. Quality control is assuring that processes are performing in an acceptable manner. TRUE

Control is used to monitor the performance of processes.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: EasyLearning Objective: 10-01 List and briefly explain the elements of the control process.Topic Area: Introduction

36. The primary purpose of statistical process control is to detect a defective product before it is shipped to a customer. FALSE

The primary purpose of SPC is to detect nonrandomness.


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37. The Taguchi Cost Function suggests that the capability ratio can be improved by extending the spread between LCL and UCL. FALSE

The Taguchi cost function suggests that reducing variation is key.


38. The variation of a sampling distribution is tighter than the variation of the underlying process distribution. TRUE

The sampling distribution exhibits less variation than the underlying process.


39. The sampling distribution can be assumed to be approximately normal even when the underlying process distribution is not normally distributed. TRUE

This is especially true as the sample size grows.


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40. Approximately 99.7% of sample means will fall within ± two standard deviations of the process mean if the process is under control. FALSE

Approximately 99.7% of sample means will fall within ± three standard deviations of the process mean.


41. The best way to assure quality is to use extensive inspection and control charts. FALSE

The best way to assure quality is to make sure processes are highly capable.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: MediumLearning Objective: 10-01 List and briefly explain the elements of the control process.Topic Area: Operations Strategy

42. Control limits are based on multiples of the process standard deviation. FALSE

Control limits are based on multiples of the standard deviation of the sample statistic.


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43. Attribute data are counted, variable data are measured. TRUE

These distinguish attribute from variable data.


44. The number of defective parts in a sample is an example of variable data because it will "vary" from one sample to another. FALSE

The number of defective parts in a sample is an example of attribute data.


45. Larger samples will require wider x-bar control limits because there is more data. FALSE

Large samples will lead to narrower control limits.


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46. When a process is not centered, its capability is measured in a slightly different way. The symbol for this case is Cpk. TRUE

Cpk is used when the process is not centered.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: EasyLearning Objective: 10-05 Assess process capability.Topic Area: Process Capability

47. Range control charts are used to monitor process central tendency. FALSE

Ranger charts monitor variability.


48. An "up and down" run test uses the median as a reference point and measures the percentage above and below the median. FALSE

An up-and-down runs test looks only at runs of increasing or decreasing values.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: EasyLearning Objective: 10-04 Perform run tests to check for nonrandomness in process output.Topic Area: Statistical Process Control

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49. "Assignable variation" is variation due to a specific cause, such as tool wear. TRUE

Assignable variation is specific cause variation.


50. Variation in a sample statistic collected from a process may be either random variation or assignable variation - or both. TRUE

Total variation can consist of both random and assignable variation.


51. "Quality of conformance" is concerned with whether a product or service conforms to its specifications. TRUE

Specification conformance is quality of conformance.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: EasyLearning Objective: 10-05 Assess process capability.Topic Area: Process Capability

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52. The larger the process variation, the tighter the specifications should be. FALSE

Greater variation would lead to wider specifications.


53. Type I and Type II errors refer to the magnitude of variation from the standard. FALSE

These refer to decisions regarding whether the process is in or out of control.


54. The greater the capability ratio, the higher the rejects. FALSE

Greater capability reduces rejects.


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55. Non-random variation is likely whenever all observations are between the LCL and UCL. FALSE

If all observations are between the LCL and UCL, then the process would be considered in control.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: HardLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control


56. Which of the following quality control sample statistics indicates a quality characteristic that is an attribute? A. meanB. varianceC. standard deviationD. rangeE. proportion

Proportions would be control with attribute control charts.


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57. A time-ordered plot of representative sample statistics is called a: A. Gantt chartB. SIMO-chartC. Control ChartD. Up-Down MatrixE. Standard deviation table

Control charts are time-ordered plots of sample statistics.


58. A control chart used to monitor the process mean is the: A. p-chartB. R-chartC. x-bar chartD. c-chartE. Gantt chart

The x-bar chart monitors the process mean.


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59. A control chart used to monitor the fraction of defectives generated by a process is the: A. p-chartB. R-chartC. x-bar chartD. c-chartE. Gantt chart

The p-chart monitors the fraction defective.


60. A p-chart would be used to monitor _______. A. average shrinkageB. dispersion in sample dataC. the fraction defectiveD. the number of defects per unitE. the range of values

The p-chart monitors the fraction defective.


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61. A c-chart is used for: A. meansB. rangesC. percent defectiveD. fraction defective per unitE. number of defects per unit

C-charts monitor the number of defects per unit.


62. A control chart used to monitor the number of defects per unit is the: A. p-chartB. R-chartC. x-bar chartD. c-chartE. Gantt chart

C-charts monitor the number of defects per unit.


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63. A point which is outside of the lower control limit on an R-chart: A. is an indication that no cause of variation is presentB. should be ignored because it signifies better than average qualityC. should be investigated because an assignable cause of variation might be presentD. should be ignored unless another point is outside that limitE. is impossible since the lower limit is always zero

Points outside of the control limits should be investigated as signals of non-random variation being present.


64. If a process is performing as it should, it is still possible to obtain observations which are outside of which limits?(I) tolerances(II) control limits(III) process variability A. IB. IIC. I and IID. II and IIIE. I, II, and III

Even capable, in control processes can have observations outside of control limits or tolerances.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: HardLearning Objective: 10-03 Use and interpret control charts.Learning Objective: 10-05 Assess process capability.Topic Area: Process CapabilityTopic Area: Statistical Process Control

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65. Which of the following relationships must always be incorrect? A. Tolerances > process variability > control limitsB. Process variability > tolerances > control limitsC. Tolerances > control limits > process variabilityD. Process variability > control limits > tolerancesE. Process variability <Tolerances<control limits

Process variability will always be greater than control limits.

AACSB: Reflective ThinkingBloom's: UnderstandDifficulty: HardLearning Objective: 10-02 Explain how control charts are used to monitor a process; and the concepts that underlie their use.Learning Objective: 10-05 Assess process capability.Topic Area: Process CapabilityTopic Area: Statistical Process Control

66. Which of the following is not a step in the quality control process? A. define what is to be controlledB. compare measurements to a standardC. eliminate each of the defects as they are identifiedD. take corrective action if necessaryE. evaluate corrective action

Eliminating defects is not part of quality control.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: HardLearning Objective: 10-01 List and briefly explain the elements of the control process.Topic Area: Introduction

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67. The probability of concluding that assignable variation exists when only random variation is present is:(I) the probability of a Type I error(II) known as the alpha risk(III) highly unlikely (IV) the sum of probabilities in the two tails of the normal distribution A. I and IIB. I and IVC. II and IIID. I, II, and IVE. I, III, and IV

Incorrect signals can be on either side of the distribution.


68. _______ variation is a variation whose cause can be identified. A. AssignableB. ControllableC. RandomD. StatisticalE. Theoretical

Assignable variation has a special cause.


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69. A plot below the lower control limit on the range chart:(I) should be ignored since lower variation is desirable(II) may be an indication that process variation has decreased(III) should be investigated for assignable cause A. I and IIB. I and IIIC. II and IIID. II onlyE. I, II, and III

Plots outside of control limits should be investigated.


70. A shift in the process mean for a measured characteristic would most likely be detected by a: A. p-chartB. x-bar chartC. c-chartD. R-chartE. s-chart

X-bar charts monitor the process mean.

AACSB: Reflective ThinkingBloom's: RememberDifficulty: EasyLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control

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71. The range chart (R-chart) is most likely to detect a change in: A. proportionB. meanC. number defectiveD. variabilityE. sample size

The range chart monitors variability.


72. The optimum level of inspection is where the: A. cost of inspection is minimumB. cost of passing defectives is minimumC. total cost of inspection and defectives is maximumD. total cost of inspection and defectives is minimumE. difference between inspection and defectives costs is minimum

At the optimum level these costs are, in total, minimized.


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73. The purpose of control charts is to: A. estimate the proportion of output that is acceptableB. weed out defective itemsC. determine if the output is within tolerances/specificationsD. distinguish between random variation and assignable variation in the processE. provide meaningful work for quality inspectors

Control charts are used to signal assignable variation.


74. The process capability index (Cpk) may mislead if:(I) the process is not stable.(II) the process output is not normally distributed.(III) the process is not centered. A. I and IIB. I and IIIC. II and IIID. II onlyE. I, II and III

When using Cpk these concerns should be addressed.


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75. A time-ordered plot of sample statistics is called a(n) ______ chart. A. StatisticalB. InspectionC. ControlD. SIMOE. Limit

A control chart is a time-ordered plot of sample statistics.


Essay Questions

76. A process that makes chocolate candy bars has an output that is normally distributed with a mean of 6 oz. and a standard deviation of .01 oz. A job is to be run that requires 200 candy bars. Determine three sigma control limits for an x-bar chart assuming a sample size of 10.If specifications are 5.98 to 6.02, what run size should be used for this job so that the expected number of good candy bars is 200, assuming the process is in control?

Approximately 210.

Feedback: The specifications are at ± 2 process standard deviations, which would include 95.44% of the output. Thus, .9544Q = 200, so Q = 209.6 or 210.

AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-05 Assess process capability.Topic Area: Process Capability

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77. Four samples of three observations each have been taken, with actual measurements (in centimeters) shown below. Construct three-sigma mean and range charts.

Control Limits are:

Feedback: Although all points are within the limits, a plot of the sample means would strongly suggest non-randomness.

AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control

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78. A town's department of public works is concerned about adverse public reaction to a sewer project that is currently in progress. Because of this, the Commissioner of Public Works has authorized a weekly survey to be conducted of town residents. Each week, a sample of 100 residents is questioned on their feelings towards the project. The results to date are shown below. Analyze this data using control charts that would provide for a 5% risk of Type I error.

Feedback: Sentiment appears to be stable, in that none of the eight weeks is outside these limits.


79. Construct the appropriate two-sigma control chart for the sample observations listed below.

Feedback: Observation 1 is outside this interval.


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80. Perform run tests on the given data. What can you conclude?

Feedback: Neither pattern indicates any concern with regard to non-randomness.

AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-04 Perform run tests to check for nonrandomness in process output.Topic Area: Statistical Process Control

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81. The chart below depicts 16 sample means that were taken at periodic intervals and plotted on a control chart. Does the output appear to be random?

Since all points are within the control limits, this suggests an in-control process. To determine whether it is truly random, runs tests should be performed.The expected number of above/below runs would be:

Feedback: Neither pattern indicates any concern with regard to non-randomness.

AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Learning Objective: 10-04 Perform run tests to check for nonrandomness in process output.Topic Area: Statistical Process Control

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82. Given the following control chart, would you say that the process appears to be performing appropriately?

Since all points are within the control limits, this suggests an in-control process. To determine whether it is truly random, runs tests should be performed.The expected number of above/below runs would be:

Feedback: The up-down runs test indicates a non-random process. There seems to be too great a tendency for this process to drift upward.

AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Learning Objective: 10-04 Perform run tests to check for nonrandomness in process output.Topic Area: Statistical Process Control

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83. An analyst has gathered data and counted the number of runs with respect to the median. There were 60 observations and 22 runs. What can the analyst conclude given this information?

The expected number of above/below runs would be

Feedback: This exceeds the generally accepted threshold of |2.00|, so we would conclude that there are too few runs to consider these data random.


84. An operator collected the following time series data from a process:

(A) Determine the number of A/B runs.(B) Determine the number of up/down runs.

There are 6 above-below runs: B A B A A B B AThere are 5 up/down runs: U D U U D D U

Feedback: Use the calculated median of 4.35.


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85. An analyst counted 17 A/B runs and 15 U/D runs in 26 time series observations. Do these results suggest that the data are non-random?

These results do not suggest the data are non-random because neither of the Z-values exceeds the accepted threshold of |2.00|.

Feedback: These results do not suggest the data are non-random because neither of the Z-values exceeds the accepted threshold of |2.00|.



86. The number of runs up and down for the data above is: A. 3B. 4C. 5D. 6E. none of these

Count the number of up and down runs.


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Count the number of runs above or below the median.

AACSB: AnalyticBloom's: ApplyDifficulty: HardLearning Objective: 10-04 Perform run tests to check for nonrandomness in process output.Topic Area: Statistical Process Control

The following data occurs chronologically from left to right:


The sample median is 15.2.

AACSB: AnalyticBloom's: ApplyDifficulty: HardLearning Objective: 10-04 Perform run tests to check for nonrandomness in process output.Topic Area: Statistical Process Control

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89. The number of runs up and down is: A. 2B. 3C. 4D. 5E. none of these

Count the number of up and down runs.


A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results:

90. What is the sample mean service life for sample 2? A. 460 hoursB. 495 hoursC. 500 hoursD. 515 hoursE. 525 hours

Average the four observations.


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91. What is the mean of the sampling distribution of sample means when service life is in control? A. 250 hoursB. 470 hoursC. 495 hoursD. 500 hoursE. 515 hours

Average the sample means.


92. What is the standard deviation of the sampling distribution of sample means for whenever service life is in control? A. 5 hoursB. 6.67 hoursC. 10 hoursD. 11.55 hoursE. 20 hours

Use the central limit theorem.

AACSB: AnalyticBloom's: ApplyDifficulty: HardLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control

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93. If he uses upper and lower control limits of 520 and 480 hours, what is his risk (alpha) of concluding service life is out of control when it is actually under control (Type I error)? A. 0.0026B. 0.0456C. 0.3174D. 0.6826E. 0.9544

These are two-sigma limits.


94. If he uses upper and lower control limits of 520 and 480 hours, on what sample(s) (if any) does service life appear to be out of control? A. sample 1B. sample 2C. sample 3D. both samples 2 and 3E. all samples are in control

Sample 3's sample mean is below the lower control limit.


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A Quality Analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that whenever this process is under control, package weight is normally distributed with a mean of twenty ounces and a standard deviation of two ounces. Each day last week, he randomly selected four packages and weighed each:

95. What is the sample mean package weight for Thursday? A. 19 ouncesB. 20 ouncesC. 20.6 ouncesD. 21 ouncesE. 23 ounces

Average the four values.


96. What is the mean of the sampling distribution of sample means when this process is under control? A. 18 ouncesB. 19 ouncesC. 20 ouncesD. 21 ouncesE. 22 ounces

When the process is in control, this is its mean value.


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97. What is the standard deviation of the sampling distribution of sample means for whenever this process is under control? A. 0.1 ouncesB. 0.4 ouncesC. 0.5 ouncesD. 1 ounceE. 2 ounces

Use the central limit theorem.

AACSB: AnalyticBloom's: RememberDifficulty: HardLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control

98. If he uses upper and lower control limits of 22 and 18 ounces, what is his risk (alpha) of concluding this process is out of control when it is actually in control (Type I error)? A. 0.0026B. 0.0456C. 0.3174D. 0.6826E. 0.9544



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99. If he uses upper and lower control limits of 22 and 18 ounces, on what day(s), if any, does this process appear to be out of control? A. MondayB. TuesdayC. Monday and TuesdayD. Monday, Tuesday, and ThursdayE. none

This day's sample average is outside of the control limits.


A Quality Analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results:

100. What is the sample mean for machine #1? A. 15B. 16C. 17D. 21E. 23

Average the four values.


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101. What is the estimate of the process mean for whenever it is under control? A. 16B. 19C. 20D. 21E. 23

Average the sample averages.


102. What is the estimate of the sample average range based upon this limited sample? A. 13.0B. 4.33C. 5.4D. 4.2E. 2.0

Average the sample ranges.


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103. What are the x-bar chart three sigma upper and lower control limits? A. 22 and 18B. 23.29 and 16.71C. 23.5 and 16.5D. 23.16 and 16.84E. 24 and 16

Use control chart factors of a sample size of four.


104. For upper and lower control limits of 23.29 and 16.71, which machine(s), if any, appear(s) to have an out-of-control process mean? A. machine #1B. machine #2C. machine #3D. all of the machinesE. none of the machines

This machine's sample average fell outside the control limits.


The Chair of the Operations Management Department at Quality University wants to construct a p-chart for determining whether the four faculty teaching the basic P/OM course are under control with regard to the number of students who fail the course. Accordingly, he sampled 100 final grades from last year for each instructor, with the following results:

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105. What is the sample proportion of failures (p) for Prof. D? A. 0B. .04C. .11D. .13E. .16

Divide the number of failures by the sample size.


106. What is the estimate of the mean proportion of failures for these instructors? A. .10B. .11C. .13D. .16E. .40

Average the sample proportions.


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107. What is the estimate of the standard deviation of the sampling distribution for an instructor's sample proportion of failures? A. .0075B. .03C. .075D. .3E. .75

Use the formula for the standard deviation of the sample proportion.


108. What are the .95 (5% risk of Type I error) upper and lower control limits for the p-chart? A. .95 and .05B. .13 and .07C. .1588 and .0412D. .16 and .04E. .1774 and .0226



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109. Using .95 control limits, (5% risk of Type I error), which instructor(s), if any, should he conclude is (are) out of control? A. noneB. Prof. BC. Prof. DD. both Prof. B and Prof. DE. all

These fall outside the control limits.


A Quality Analyst wants to construct a control chart for determining whether four machines, all producing the same product, are under control with regard to a particular quality attribute. Accordingly, she inspected 1,000 units of output from each machine in random samples, with the following results:

110. What is the sample proportion of defectives for machine #1? A. .023B. .02C. .0115D. .0058E. .005

Divide the number of defectives by the sample size.


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111. What is the estimate of the process proportion of defectives for whenever it is under control? A. .08B. .06C. .04D. .02E. .01

Average the sample proportions.


112. What is the estimate of the standard deviation of the sampling distribution of sample proportions for whenever this process is under control? A. .016B. .00016C. .04D. .0044E. .00002

Use the formula for the standard deviation of the sample proportions.


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113. What are the control chart upper and lower control limits for an alpha risk of .05? A. .0272 and .0128B. .0287 and .0113C. .029 and .013D. .0303 and .0097E. .0332 and .0068



114. For upper and lower control limits of .026 and .014, which machine(s), if any, appear(s) to be out-of-control for process proportion of defectives? A. machine #3B. machine #4C. machines #3 and #4D. machines #2 and #3E. none of the machines

The sample proportions of these samples fall outside the control limits.


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Essay Questions

Given the following process control data for a normally distributed quality variable (three samples of size four each):

115. What is the sample mean for sample #1? #2? #3?

14; 17.5; 16.5

Feedback: Average the observations taken in each sample.


116. If the process is known to have a mean of 15 and a standard deviation of 3, what is the mean of the sampling distribution of sample means for whenever this process is under control? The standard deviation?

15; 1.5

Feedback: The sample mean average should be equal to the process mean. The sample standard deviations should be equal to the process standard deviation divided by the square root of the sample size.

AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-02 Explain how control charts are used to monitor a process; and the concepts that underlie their use.Topic Area: Statistical Process Control

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117. If the process is known to have a mean of 15 and a standard deviation of 3, what is the alpha risk (probability of Type I error) for upper and lower control limits of 16.5 and 13.5 respectively? 18 and 12? 19.5 and 10.5?

.3174; .0456; .0026

Feedback: These represent, respectively, one-, two- and three-sigma control limits.


118. If the process is known to have a mean of 15 and a standard deviation of 3, what are the three sigma upper and lower control limits for an x-bar chart?

Lower limit = 10.5Upper limit = 19.5

Feedback: This represents the process mean plus or minus three standard deviations of the sample means.


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119. If the process is known to have a mean of 15 and a standard deviation of 3, using three sigma control limits, do any of the sample means indicate an out-of-control process mean?

No, all are within the limits.

Feedback: All are within the appropriate limits.


Given the following process control data for a quality attribute (three samples of size 400 each):

120. What is the sample proportion of defectives for sample #1? #2? #3?

.09; .08; .13

Feedback: Divide the defectives by the sample size.


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121. If the process is known to produce 11 percent defectives on average, what is the mean of the sampling distribution of sample proportions for whenever this process is under control? The standard deviation?

.11; .0156

Feedback: The average of the sample means should equal the process mean.


122. If the process is known to produce 11 percent defectives on average, what is the alpha risk (probability of Type I error) for upper and lower control limits of .1256 and .0944 respectively? .1412 and .0788? .1568 and .0632?

.3174; .0456; .0026

Feedback: These represent, respectively, one-, two- and three-sigma control limits.


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123. If the process is known to produce 11 percent defectives on average, what are the upper and lower control limits for an alpha risk of .10? .05? .01?

.1357 and .0843; .1406 and .0794; .1502 and .0698

Feedback: These are found using appropriate values for Z.


124. If the process is known to produce 11 percent defectives on average, using three sigma control limits, do any of the sample proportions indicate an out-of-control process proportion of defectives?

No, all are within limits.

Feedback: All are within limits.


125. If the process proportion of defectives is unknown, what is the estimate of it?

.10.

Feedback: The sample proportion is a reasonable estimate of the population proportion.


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126. If the process proportion of defectives is unknown, what is the alpha risk (probability of Type I error) for upper and lower control limits of .115 and .085 respectively? .13 and .07? .145 and .055?

.3174; .0456; .0026

Feedback: These represent, respectively, one-, two- and three-sigma limits.


127. If the process proportion of defectives is unknown, what are the upper and lower control limits for an alpha risk of .10? .05? .01?

.1247 and .0753; .1294 and .0706; .1387 and .0613

Feedback: Use appropriate values for Z.


128. If the process proportion of defectives is unknown, using .10 alpha risk control limits, do any of the sample proportions indicate an out-of-control process proportion of defectives?

Yes: #3.

Feedback: This proportion is outside the control limits.


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A stint for use is coronary surgery requires a special coating. Specifications for this coating call for it to be at least 0.05 millimeters but no more than 0.15 millimeters.

129. If, when the coating process is in control, the long-run average is 0.09 millimeters, what metric would be used to assess this process' capability?

Cpk

Feedback: The process mean is not centered in the specification interval.

AACSB: AnalyticBloom's: ApplyDifficulty: EasyLearning Objective: 10-05 Assess process capability.Topic Area: Process Capability

130. Suppose the long-run average of this coating process is 0.09 millimeters. Further suppose this process' standard deviation is 0.015 millimeters. What proportion of the output from this process will fail to meet specifications?

0.00386

Feedback: Calculate a z-value for each specification limit relative to the parameters of this process.

AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-05 Assess process capability.Topic Area: Statistical Process Control

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131. Suppose the criterion for evaluating this process is that the appropriate capability index must be at least 1.3. With a long-run process mean of 0.09 and a standard deviation of 0.015, is this process capable?

No.

Feedback: This process Cpk equals 0.889 as it currently performs.


132. Assuming that the process mean of 0.09 cannot be changed, what process standard deviation would be required for this process to be considered capable (assuming that a capable process must have a capability index of at least 1.3)?

The process standard deviation would need to fall to approximately 0.01 to make this process capable.

Feedback: Set Cpk equal to 1.3 and then solve for the process standard deviation.

AACSB: AnalyticBloom's: ApplyDifficulty: HardLearning Objective: 10-05 Assess process capability.Topic Area: Process Capability

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133. Studies on a bottle-filling machine indicates it fills bottles to a mean of 16 ounces with a standard deviation of 0.10 ounces. What is the process specification, assuming the Cpk index of 1? A. 0.10 ouncesB. 0.20 ouncesC. 0.30 ouncesD. 16.0 ounces plus or minus 0.30 ouncesE. none of the above

Use the Cpk formula to solve for the specification interval.


134. Studies on a machine that molds plastic water pipe indicate that when it is injecting 1-inch diameter pipe, the process standard deviation is 0.05 inches. The one-inch pipe has a specification of 1-inch plus or minus 0.10 inch. What is the process capability index (Cpk) if the long-run process mean is 1 inch? A. 0.50B. 0.67C. 1.00D. 2.00E. none of the above

Use the Cpk formula to assess this process' capability.


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135. The specification limit for a product is 8 cm and 10 cm. A process that produces the product has a mean of 9.5 cm and a standard deviation of 0.2 cm. What is the process capability, Cpk? A. 3.33B. 1.67C. 0.83D. 2.50E. none of the above

Cpk is used here since the process mean isn't centered in the specification interval.


136. The specifications for a product are 6 mm ± 0.1 mm. The process is known to operate at a mean of 6.05 with a standard deviation of 0.01 mm. What is the Cpk for this process? A. 3.33B. 1.67C. 5.00D. 2.50E. none of the above

Cpk is used here since the process mean isn't centered in the specification interval.


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137. Organizations should work to improve process capability so that quality control efforts can become more ________. A. effectiveB. efficientC. necessaryD. unnecessaryE. widespread

Increasing process capability reduces the necessity for quality control.

AACSB: Reflective ThinkingBloom's: UnderstandDifficulty: MediumLearning Objective: 10-05 Assess process capability.Topic Area: Operations Strategy

138. A process results in a few defects occurring in each unit of output. Long-run, these defects should be monitored with ___________. A. p-chartsB. c-chartsC. x-bar chartsD. r-chartsE. o-charts

C-charts are used to monitor the number of defects per unit.


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139. When a process is in control, it results in there being, on average, 16 defects per unit of output. C-chart limits of 8 and 24 would lead to a _______ chance of a Type I error. A. 67%B. 92%C. 33%D. .03%E. 5%

These would be two-sigma limits

AACSB: AnalyticBloom's: ApplyDifficulty: EasyLearning Objective: 10-02 Explain how control charts are used to monitor a process; and the concepts that underlie their use.Topic Area: Statistical Process Control

140. When a process is in control, it results in there being, on average, 16 defects per unit of output. C-chart limits of 4 and 28 would lead to a _______ chance of a Type I error. A. 67%B. 92%C. 33%D. 0.3%E. 5%

These would be three-sigma limits.

AACSB: AnalyticBloom's: ApplyDifficulty: EasyLearning Objective: 10-02 Explain how control charts are used to monitor a process; and the concepts that underlie their use.Topic Area: Statistical Process Control

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141. The basis for a statistical process control chart is a(the) __________. A. process capabilityB. sampling distributionC. control limitD. sample rangeE. sample mean

Control charts reflect the sampling distribution of an in control process.


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jee maths exam for nov-om

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