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?
Multiple Choice Questions
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:
88. The number of runs with respect to the sample median is: A. 2B. 3C. 4D. 5E. none of these
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)?
Multiple Choice Questions
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.
AACSB: Reflective ThinkingBloom's: RememberDifficulty: MediumLearning Objective: 10-01 List and briefly explain the elements of the control process.Topic Area: 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.
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
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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.
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
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.
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
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.
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
18. Range charts are used mainly with attribute data. FALSE
Range charts are used with variable data.
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
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19. Range charts and p-charts are both used for variable data. FALSE
P-charts are used with attribute data.
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
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.
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
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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Chapter 10 - Quality Control
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.
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
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.
AACSB: Reflective ThinkingBloom's: RememberDifficulty: HardLearning Objective: 10-05 Assess process capability.Topic Area: Process Capability
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Chapter 10 - Quality Control
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.
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
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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Chapter 10 - Quality Control
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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Chapter 10 - Quality Control
31. Statistical process control focuses on the acceptability of process output. FALSE
Statistical process control focuses on the variability of processes.
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
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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Chapter 10 - Quality Control
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.
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
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Chapter 10 - Quality Control
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.
AACSB: Reflective ThinkingBloom's: RememberDifficulty: HardLearning Objective: 10-05 Assess process capability.Topic Area: Process Capability
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.
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
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.
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
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Chapter 10 - Quality Control
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.
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
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.
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
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Chapter 10 - Quality Control
43. Attribute data are counted, variable data are measured. TRUE
These distinguish attribute from variable data.
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
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.
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
45. Larger samples will require wider x-bar control limits because there is more data. FALSE
Large samples will lead to narrower control limits.
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
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Chapter 10 - Quality Control
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.
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
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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Chapter 10 - Quality Control
49. "Assignable variation" is variation due to a specific cause, such as tool wear. TRUE
Assignable variation is specific cause variation.
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
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.
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
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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Chapter 10 - Quality Control
52. The larger the process variation, the tighter the specifications should be. FALSE
Greater variation would lead to wider specifications.
AACSB: Reflective ThinkingBloom's: RememberDifficulty: HardLearning Objective: 10-05 Assess process capability.Topic Area: Process Capability
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.
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
54. The greater the capability ratio, the higher the rejects. FALSE
Greater capability reduces rejects.
AACSB: Reflective ThinkingBloom's: RememberDifficulty: HardLearning Objective: 10-05 Assess process capability.Topic Area: Process Capability
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Chapter 10 - Quality Control
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
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
Proportions would be control with attribute control charts.
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
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Chapter 10 - Quality Control
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.
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
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.
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
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Chapter 10 - Quality Control
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.
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
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.
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
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Chapter 10 - Quality Control
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.
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
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.
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
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Chapter 10 - Quality Control
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.
AACSB: Reflective ThinkingBloom's: RememberDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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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Chapter 10 - Quality Control
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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Chapter 10 - Quality Control
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.
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
68. _______ variation is a variation whose cause can be identified. A. AssignableB. ControllableC. RandomD. StatisticalE. Theoretical
Assignable variation has a special cause.
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
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Chapter 10 - Quality Control
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.
AACSB: Reflective ThinkingBloom's: RememberDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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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Chapter 10 - Quality Control
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.
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
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.
AACSB: Reflective ThinkingBloom's: RememberDifficulty: MediumLearning Objective: 10-01 List and briefly explain the elements of the control process.Topic Area: Inspection
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Chapter 10 - Quality Control
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.
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
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.
AACSB: Reflective ThinkingBloom's: RememberDifficulty: HardLearning Objective: 10-05 Assess process capability.Topic Area: Process Capability
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Chapter 10 - Quality Control
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.
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
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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Chapter 10 - Quality 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.
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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Chapter 10 - Quality Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
79. Construct the appropriate two-sigma control chart for the sample observations listed below.
Feedback: Observation 1 is outside this interval.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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Chapter 10 - Quality Control
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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Chapter 10 - Quality Control
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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Chapter 10 - Quality Control
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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Chapter 10 - Quality Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-04 Perform run tests to check for nonrandomness in process output.Topic Area: Statistical Process Control
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.
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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Chapter 10 - Quality Control
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|.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-04 Perform run tests to check for nonrandomness in process output.Topic Area: Statistical Process Control
Multiple Choice Questions
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.
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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Chapter 10 - Quality Control
87. The number of runs with respect to the sample median is: A. 3B. 4C. 5D. 6E. none of these
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:
88. The number of runs with respect to the sample median is: A. 2B. 3C. 4D. 5E. none of these
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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Chapter 10 - Quality Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-04 Perform run tests to check for nonrandomness in process output.Topic Area: Statistical Process Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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Chapter 10 - Quality Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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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Chapter 10 - Quality Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: HardLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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Chapter 10 - Quality 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
Average the four values.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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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
These are two-sigma limits.
AACSB: AnalyticBloom's: ApplyDifficulty: HardLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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Chapter 10 - Quality Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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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Chapter 10 - Quality Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
106. What is the estimate of the mean proportion of failures for these instructors? A. .10B. .11C. .13D. .16E. .40
Average the sample proportions.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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Chapter 10 - Quality Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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
These are two-sigma limits.
AACSB: AnalyticBloom's: ApplyDifficulty: HardLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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Chapter 10 - Quality Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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Chapter 10 - Quality Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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Chapter 10 - Quality Control
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
These are two-sigma limits.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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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Chapter 10 - Quality Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: HardLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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Chapter 10 - Quality Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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Chapter 10 - Quality Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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Chapter 10 - Quality Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: HardLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-03 Use and interpret control charts.Topic Area: Statistical Process Control
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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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-05 Assess process capability.Topic Area: Process Capability
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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Multiple Choice Questions
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-05 Assess process capability.Topic Area: Process Capability
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.
AACSB: AnalyticBloom's: ApplyDifficulty: MediumLearning Objective: 10-05 Assess process capability.Topic Area: 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.
AACSB: AnalyticBloom's: ApplyDifficulty: HardLearning Objective: 10-05 Assess process capability.Topic Area: Process Capability
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.
AACSB: AnalyticBloom's: ApplyDifficulty: HardLearning Objective: 10-05 Assess process capability.Topic Area: Process Capability
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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.
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
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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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Chapter 10 - Quality Control
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.
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
10-97
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