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Quality 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
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
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
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
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
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
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
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. mean
B. variance
C. standard deviation
D. range
E. proportion
57. A time-ordered plot of representative sample statistics is called a:
A. Gantt chart
B. SIMO-chart
C. Control Chart
D. Up-Down Matrix
E. Standard deviation table
58. A control chart used to monitor the process mean is the:
A. p-chart
B. R-chart
C. x-bar chart
D. c-chart
E. Gantt chart
59. A control chart used to monitor the fraction of defectives generated by a process is the:
A. p-chart
B. R-chart
C. x-bar chart
D. c-chart
E. Gantt chart
60. A p-chart would be used to monitor _______.
A. average shrinkage
B. dispersion in sample data
C. the fraction defective
D. the number of defects per unit
E. the range of values
61. A c-chart is used for:
A. means
B. ranges
C. percent defective
D. fraction defective per unit
E. number of defects per unit
62. A control chart used to monitor the number of defects per unit is the:
A. p-chart
B. R-chart
C. x-bar chart
D. c-chart
E. 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 present
B. should be ignored because it signifies better than average quality
C. should be investigated because an assignable cause of variation might be present
D. should be ignored unless another point is outside that limit
E. is impossible since the lower limit is always zero
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. I
B. II
C. I and II
D. II and III
E. I, II, and III
65. Which of the following relationships must always be incorrect?
A. Tolerances > process variability > control limits
B. Process variability > tolerances > control limits
C. Tolerances > control limits > process variability
D. Process variability > control limits > tolerances
E. 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 controlled
B. compare measurements to a standard
C. eliminate each of the defects as they are identified
D. take corrective action if necessary
E. 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 II
B. I and IV
C. II and III
D. I, II, and IV
E. I, III, and IV
68. _______ variation is a variation whose cause can be identified.
A. Assignable
B. Controllable
C. Random
D. Statistical
E. 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 II
B. I and III
C. II and III
D. II only
E. I, II, and III
70. A shift in the process mean for a measured characteristic would most likely be detected by a:
A. p-chart
B. x-bar chart
C. c-chart
D. R-chart
E. s-chart
71. The range chart (R-chart) is most likely to detect a change in:
A. proportion
B. mean
C. number defective
D. variability
E. sample size
72. The optimum level of inspection is where the:
A. cost of inspection is minimum
B. cost of passing defectives is minimum
C. total cost of inspection and defectives is maximum
D. total cost of inspection and defectives is minimum
E. difference between inspection and defectives costs is minimum
73. The purpose of control charts is to:
A. estimate the proportion of output that is acceptable
B. weed out defective items
C. determine if the output is within tolerances/specifications
D. distinguish between random variation and assignable variation in the process
E. 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 II
B. I and III
C. II and III
D. II only
E. I, II and III
75. A time-ordered plot of sample statistics is called a(n) ______ chart.
A. Statistical
B. Inspection
C. Control
D. SIMO
E. Limit
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.
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.
80. Perform run tests on the given data. What can you conclude?
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?
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?
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. 3
B. 4
C. 5
D. 6
E. none of these
87. The number of runs with respect to the sample median is:
A. 3
B. 4
C. 5
D. 6
E. 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. 2
B. 3
C. 4
D. 5
E. none of these
89. The number of runs up and down is:
A. 2
B. 3
C. 4
D. 5
E. 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:
90. What is the sample mean service life for sample 2?
A. 460 hours
B. 495 hours
C. 500 hours
D. 515 hours
E. 525 hours
91. What is the mean of the sampling distribution of sample means when service life is in control?
A. 250 hours
B. 470 hours
C. 495 hours
D. 500 hours
E. 515 hours
92. What is the standard deviation of the sampling distribution of sample means for whenever service life is in control?
A. 5 hours
B. 6.67 hours
C. 10 hours
D. 11.55 hours
E. 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. 0.0026
B. 0.0456
C. 0.3174
D. 0.6826
E. 0.9544
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 1
B. sample 2
C. sample 3
D. both samples 2 and 3
E. 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 ounces
B. 20 ounces
C. 20.6 ounces
D. 21 ounces
E. 23 ounces
96. What is the mean of the sampling distribution of sample means when this process is under control?
A. 18 ounces
B. 19 ounces
C. 20 ounces
D. 21 ounces
E. 22 ounces
97. What is the standard deviation of the sampling distribution of sample means for whenever this process is under control?
A. 0.1 ounces
B. 0.4 ounces
C. 0.5 ounces
D. 1 ounce
E. 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. 0.0026
B. 0.0456
C. 0.3174
D. 0.6826
E. 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. Monday
B. Tuesday
C. Monday and Tuesday
D. Monday, Tuesday, and Thursday
E. 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:
100. What is the sample mean for machine #1?
A. 15
B. 16
C. 17
D. 21
E. 23
101. What is the estimate of the process mean for whenever it is under control?
A. 16
B. 19
C. 20
D. 21
E. 23
102. What is the estimate of the sample average range based upon this limited sample?
A. 13.0
B. 4.33
C. 5.4
D. 4.2
E. 2.0
103. What are the x-bar chart three sigma upper and lower control limits?
A. 22 and 18
B. 23.29 and 16.71
C. 23.5 and 16.5
D. 23.16 and 16.84
E. 24 and 16
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 #1
B. machine #2
C. machine #3
D. all of the machines
E. 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. 0
B. .04
C. .11
D. .13
E. .16
106. What is the estimate of the mean proportion of failures for these instructors?
A. .10
B. .11
C. .13
D. .16
E. .40
107. What is the estimate of the standard deviation of the sampling distribution for an instructor’s sample proportion of failures?
A. .0075
B. .03
C. .075
D. .3
E. .75
108. What are the .95 (5% risk of Type I error) upper and lower control limits for the p-chart?
A. .95 and .05
B. .13 and .07
C. .1588 and .0412
D. .16 and .04
E. .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. none
B. Prof. B
C. Prof. D
D. both Prof. B and Prof. D
E. 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:
110. What is the sample proportion of defectives for machine #1?
A. .023
B. .02
C. .0115
D. .0058
E. .005
111. What is the estimate of the process proportion of defectives for whenever it is under control?
A. .08
B. .06
C. .04
D. .02
E. .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. .016
B. .00016
C. .04
D. .0044
E. .00002
113. What are the control chart upper and lower control limits for an alpha risk of .05?
A. .0272 and .0128
B. .0287 and .0113
C. .029 and .013
D. .0303 and .0097
E. .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 #3
B. machine #4
C. machines #3 and #4
D. machines #2 and #3
E. 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?
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):
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?
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?
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?
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. lower spec = 0.1 ounces and upper spec = 1 ounce
B. lower spec = 8.7 ounces and upper spec = 12.5 ounces
C. lower spec = 12.0 ounces and upper spec = 21.4 ounces
D. lower spec = 15.7 ounces and upper spec = 16.3 ounces
E. none of these
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. 0.50
B. 0.67
C. 1.00
D. 2.00
E. 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. 3.33
B. 1.67
C. 0.83
D. 2.50
E. 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. 3.33
B. 1.67
C. 5.00
D. 2.50
E. none of the above
137. Organizations should work to improve process capability so that quality control efforts can become more ________.
A. effective
B. efficient
C. necessary
D. unnecessary
E. widespread
138. A process results in a few defects occurring in each unit of output. Long-run, these defects should be monitored with ___________.
A. p-charts
B. c-charts
C. x-bar charts
D. r-charts
E. 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 capability
B. sampling distribution
C. control limit
D. sample range
E. sample mean
Question Answer: