File: ch03, chapter 3: Statistical Quality Control
True/False
1. Statistical process control involves monitoring and controlling a process to
prevent poor quality.
Ans: True, LO: 1, Bloom: K, Difficulty: Easy, AACSB: None,
2. Statistical process control is based on a philosophy of inspection as opposed to
prevention.
Ans: False, LO: 1, Bloom: K, Difficulty: Moderate, AACSB: None
3. One goal of statistical process control is to prevent a process from producing
items that have to be scrapped or reworked.
Ans: True, LO: 1, Bloom: K, Difficulty: Easy, AACSB: None
4. Two types of variation associated with the output of a process are common
cause (random) and special cause (nonrandom).
Ans: True, LO: 1, Bloom: K, Difficulty: Easy, AACSB: None
5. Control limits are based on the special cause (nonrandom) variation inherent in
a process.
Ans: False, LO: 1, Bloom: K, Difficulty: Moderate, AACSB: None
6. A process that is determined to be in control contains no variation.
Ans: False, LO: 1, Bloom: K, Difficulty: Easy, AACSB: None
7. Common cause (random) variation provides evidence that the process is not in
control.
Ans: False, LO: 1, Bloom: K, Difficulty: Easy, AACSB: None
8. After special cause variation is detected, the focus changes to identifying the
root cause of the variation and eliminating it.
Ans: True, LO: 1, Bloom: K, Difficulty: Hard, AACSB: None
9. Process control is achieved by taking periodic samples from a process and
plotting the sample points on a chart to determine if the process is within
control limits.
Ans: True, LO: 2, Bloom: K, Difficulty: Moderate, AACSB: None
10. When a control chart detects no special cause (nonrandom) variation in a
process, the upper and lower control limits are the same value.
Ans: False, LO: 2, Bloom: K, Difficulty: Hard, AACSB: None
11. It is sometimes not necessary to determine new control limits after special
cause (nonrandom) variation has been identified if the source has been
eliminated without changing the process.
Ans: True, LO: 2, Bloom: K, Difficulty: Hard, AACSB: None
12. A variable measure classifies while an attribute measure quantifies.
Ans: False, LO: 2, Bloom: K, Difficulty: Moderate, AACSB: None
13. With a c-chart, the sample size is small and may contain only one item.
Ans: True, LO: 3, Bloom: K, Difficulty: Easy, AACSB: None
14. A p-chart is used to monitor the proportion defective in the output of a
process.
Ans: True, LO: 3, Bloom: K, Difficulty: Easy, AACSB: None
15. Attribute control charts are used to monitor descriptive characteristics of the
output of a process rather than measurable characteristics.
Ans: True, LO:3, Bloom: K, Difficulty: Easy, AACSB: None
16. The formula used to determine the upper and lower control limits are based on
product specification limits.
Ans: False, LO: 4, Bloom: K, Difficulty: Easy, AACSB: None
17. Variable control charts are used to monitor measurable characteristics of a
process’s outputs rather than descriptive characteristics.
Ans: True, LO: 4, Bloom: K, Difficulty: Easy, AACSB: None
18. An x-bar and R-chart constructed to monitor and control a process use the
same raw data.
Ans: True, LO: 4, Bloom: K, Difficulty: Moderate, AACSB: None
19. Variable control charts are used for quantitative measures such as weight or
time.
Ans: True, LO: 4, Bloom: K, Difficulty: Moderate, AACSB: None

20. Construction and use of an x -chart is based on an assumption that the sample
points are normally distributed around the centerline.
Ans: True, LO: 4, Bloom: K, Difficulty: Hard, AACSB: None
21. The range is the difference between the smallest and largest values in a
sample.
Ans: True, LO: 4, Bloom: K, Difficulty: Easy, AACSB: None
22. The range measures the variation within samples versus the variation between
samples.
Ans: True, LO: 4, Bloom: K, Difficulty: Moderate, AACSB: None
23. It is possible to have low variation within samples while at the same time
having high variation between sample means.
Ans: True, LO: 4, Bloom: K, Difficulty: Moderate, AACSB: None
24. One advantage of using a pattern test is that special cause variations may be
identified before any points are plotted outside the control limits.
Ans: True, LO: 5, Bloom: K, Difficulty: Moderate, AACSB: None
25. A pattern test can identify an out-of-control process even if all sample points
are within control limits.
Ans: True, LO: 5, Bloom: K, Difficulty: Moderate, AACSB: None
26. A control chart is in control when the plot of the sample points exhibits a
pattern.
Ans: False, LO: 5, Bloom: K, Difficulty: Moderate, AACSB: None
27. If the points plotted on a control chart display a pattern, it is called a run.
Ans: True, LO: 5, Bloom: K, Difficulty: Moderate, AACSB: None
28. When constructing a control chart for the first time, all points should be within
the control limits indicating the process is in control.
Ans: True, LO: 5, Bloom: K, Difficulty: Moderate, AACSB: None
29. Process control charts are often used at a critical point after which it is
difficult to correct or rework the process output.
Ans: True, LO: 5, Bloom: K, Difficulty: Moderate, AACSB: None
30. Control charts visually show when a process is not within statistical control
limits.
Ans: True, LO: 5, Bloom: K, Difficulty: Easy, AACSB: None
31. The popularity of Excel and other data analysis software has been a major
factor in the increased use of statistical process control.
Ans: True, LO: 6, Bloom: K, Difficulty: Moderate, AACSB: None
32. Tolerances or specification limits are allowable variation prescribed in a
product design.
Ans: True, LO: 7, Bloom: K, Difficulty: Moderate, AACSB: None
33. Tolerances reflect the amount of common cause variation allowed in a
process.
Ans: False, LO: 7, Bloom: K, Difficulty: Moderate, AACSB: None
34. For a given process, the process capability ratio is not related to its
specification limits.
Ans: False, LO: 7, Bloom: K, Difficulty: Moderate, AACSB: None
35. A process capability ratio greater than one shows that a process is capable of
producing output within its specification limits.
Ans: True, LO: 7, Bloom: K, Difficulty: Moderate, AACSB: None
36. All processes contain a certain amount of variation in their output.
Ans: True, LO: 7, Bloom: K, Difficulty: Easy, AACSB: None
37. A sequence of sample points that display a pattern is known as a run.
Ans: True, LO: 7, Bloom: K, Difficulty: Easy, AACSB: None
38. Statistical process control can prevent poor quality before it occurs if a pattern
is evident in the plotted points.
Ans: True, LO: 7, Bloom: K, Difficulty: Moderate, AACSB: None
39. The process capability index indicates how much a process mean differs from
the target specification value.
Ans: True, LO: 7, Bloom: K, Difficulty: Moderate, AACSB: None
Multiple Choice Questions
40. If a sample point plotted on a control chart is outside the control limits
a. the evidence indicates the process is in control.
b. the evidence indicates the process is out of control.
c. the evidence is inconclusive.
d. None of these answer choices is correct.
Ans: B, LO: 1, Bloom: K, Difficulty: Moderate, AACSB: None.
41. Which of the following could be responsible for variability that is special
cause (nonrandom)?
a. Broken machinery.
b. Defective parts and materials.
c. Operator error.
d. All these answer choices are correct.
Ans: D, LO: 1, Bloom: K, Difficulty: Hard, AACSB: None
42. Common (random) variation of a process depends on all the following except
a. errors due to lack of training.
b. the equipment and machinery used.
c. the operator.
d. system used for measurement.
Ans: A, LO: 1, Bloom: K, Difficulty: Hard, AACSB: None
43. An attribute measure is a product characteristic such
a. weight.
b. color.
c. length.
d. time.
Ans: B, LO: 1, Bloom: K, Difficulty: Moderate, AACSB: None
44. A variable measure is a product characteristic such as
a. color.
b. smooth.
c. temperature
d. tastes good
Ans: C, LO: 1, Bloom: K, Difficulty: Moderate, AACSB: None
45. Which of the following services can be measured and monitored with control
charts?
a. Hospitals
b. Airlines
c. Banks
d. All these answer choices are correct.
Ans: D, LO: 2, Bloom: K, Difficulty: Easy, AACSB: None
46. Control charts are typically used at the ___________ of a process.
a. beginning.
b. middle.
c. end.
d. All these answer choices are correct.
Ans: A, LO: 2, Bloom: K, Difficulty: Moderate, AACSB: None
a.
b.
c.
d.
47. Which of the following is not a primary purpose of statistical process control?
to establish control limits
to detect special cause variations
to identify specification limits
to determine when a process is not in control
Ans: C, LO:2, Bloom: K, Difficulty: Easy, AACSB: None
48. Four common types of control charts include all of the following except:

a.
b.
c.
d.
x -chart
t-chart
p-chart
c-chart
Ans: B, LO: 2, Bloom: K, Difficulty: Easy, AACSB: None
49. Which of the following is not a characteristic of a control chart?
a.
the centerline is determined using special cause (nonrandom) variations.
b.
the upper and lower control limits are based on special cause (nonrandom)
variation.
c.
the centerline is determined by using the target value.
d.
None of these answer choices is correct.
Ans: D, LO: 2, Bloom: K, Difficulty: Hard, AACSB: None
a.
b.
c.
d.
50. Special cause (nonrandom) variation in a process is more likely to be detected
with
wider control limits
narrow control limits
wider specification limits
narrow specification limits
Ans: B, LO: 2, Bloom: K, Difficulty: Moderate, AACSB: None
51. Which of the following statements concerning control chart limits is true?
a. the smaller the value of z, the more narrow the control limits are and the more
sensitive the chart is to changes in the production process
b. the larger the value of z, the more narrow the control limits are and the more
sensitive the chart is to changes in the production process
c. the smaller the value of z, the wider the control limits are and the less
sensitive the chart is to changes in the production process
d. the larger the value of z, the more narrow the control limits are and the less
sensitive the chart is to changes in the production process
Ans: A, LO: 2, Bloom: K, Difficulty: Hard, AACSB: None
52. The basic purpose of control charts include(s)
a. establishing control limits for a process.
b. monitoring the process to indicate when it is out of control.
c. both establishing control limits for a process and monitoring the process to
indicate when it is out of control are basic purposes.
d. None of these answer choices is correct.
Ans: C, LO: 2, Bloom: K, Difficulty: Easy, AACSB: None
53. The formulas for determining the upper and lower control limits are based on
the number of standard deviations, z, from the process average. Management
usually selects a z value of _______.
a. one
b. two
c. three
d. six
Ans: C, LO:2, Bloom: K, Difficulty: Moderate, AACSB: None
54. When a control chart is first developed, if the process is found to be out of
control,
a. the control chart can be utilized.
b. the control chart should not be utilized until more samples are taken,
c. the process should be examined and corrections made before a new control
chart is constructed.
d. the process should be replaced by a new process.
Ans: C, LO: 2, Bloom: K, Difficulty: Moderate, AACSB: None
55. A control chart that uses the actual number of defects per item to monitor a
process is known as a
a. p-chart
b. c-chart
c. R-chart

x -chart
d.
Ans: B, LO: 3, Bloom: K, Difficulty: Moderate, AACSB: None
56. If a sample of 40 units of output found 500 defects, then the center line for
monitoring the average number of defects per unit of output would be

a. c = 40

b. c = 0.08

c. c = 12.5

d. c = 20,000
Ans: C, LO: 3, Bloom: K, Difficulty: Moderate, AACSB: None
Solution: centerline=500/40
57. If a sample of 40units of output found 500 defects, then the 3-sigma upper

control limit for the c chart would be
a. 12.50
b. 23.11
c. 37.50
d. 75.00
Ans: B, LO: 3, Bloom: K, Difficulty: Moderate, AACSB: None
Solution: UCL=12.5+3*SQRT(12.5) =23.11
58. A company randomly selects 100 light bulbs every day for 40 days from its
production process. If 600 defective light bulbs are found in the sampled bulbs then
the estimate for the average percent defective would be
a. 6.667
b. 0.167
c. 0.150
d. 0.250
Ans: C, LO:3, Bloom: K, Difficulty: Moderate, AACSB: None
Solution: process average= 600/(100*40)=0.15
59. A company randomly selects 100 light bulbs every day for 40 days from its
production process. If 600 defective light bulbs are found in the sampled bulbs then
the 3-sigma lower control limit would be
a. 0.0357
b. 0.0429
c. 0.1500
d. 0.1857
Ans: B, LO: 32, Bloom: K, Difficulty: Moderate, AACSB: None
Solution: LCL=.15-3*SQRT(.15*.85/100)=.0429
60. Which of the following control charts is based on the number of defects within a
sample?

a.
b.
c.
d.
x
R
c
p
Ans: C, LO:3, Bloom: K, Difficulty: Moderate, AACSB: None
61. Which of the following control charts is used to monitor the percent of defective
items within a sample?

a.
b.
c.
d.
x
R
c
p
Ans: D, LO: 3, Bloom: K, Difficulty: Easy, AACSB: None
62. If the quality of a process’s output is determined by classifying the output as
being defective or not defective, use a(n) ________control chart.

a.
b.
c.
d.
x
R
c
p
Ans: D, LO: 3, Bloom: K, Difficulty: Moderate, AACSB: None
63. Which of the following control charts are based on sample sizes as small as
one?

a.
b.
c.
d.
x
R
c
p
Ans: C, LO: 3, Bloom: K, Difficulty: Moderate, AACSB: None
64. Which of the following control charts are often based on sample sizes equal to
or larger than one hundred?

a.
b.
c.
d.
x
R
c
p
Ans: D, LO: 3, Bloom: K, Difficulty: Moderate, AACSB: None
65. Consider a production process that produces batteries. A quality engineer has
taken 20 samples each containing 100 batteries. The total number of defective
batteries observed over the 20 samples is 200. The centerline for the control
chart constructed using z equal to two is
a. 0.03
b. 0.04
c. 0.05
d. 0.10
Ans: D, LO: 3, Bloom: K, Difficulty: Easy, AACSB: None
Solution: 2100/(20*100)=0.10
66. Consider a production process that produces batteries. A quality engineer has
taken 20 samples each containing 100 batteries. The total number of defective
batteries observed over the 20 samples is 200. The sample standard deviation
is
a. 0.03
b. 0.04
c. 0.05
d. 0.10
Ans: A, LO: 3, Bloom: K, Difficulty: Easy, AACSB: None
Solution: SQRT(.10*.90/100) = .03
67. Consider a production process that produces batteries. A quality engineer has
taken 20 samples each containing 100 batteries. The total number of defective
batteries observed over the 20 samples is 200. The UCL for the control chart
constructed using two sigma is
a. 0.088
b. 0.094
c. 0.104
d. 0.160
Ans: D, LO: 3, Bloom: K, Difficulty: Easy, AACSB: None
Solution: UCL=.10+2*.03=.160
68. Consider a production process that produces batteries. A quality engineer has
taken 20 samples each containing 100 batteries. The total number of defective
batteries observed over the 20 samples is 200. The LCL for the control chat
constructed using two sigma is
a. 0.01
b. 0.04
c. 0. 12
d. 0.16
Ans: B, LO:3, Bloom: K, Difficulty: Easy, AACSB: None
Solution: LCL=.10-2*.03=.04
69. Consider a production process that produces tires. A quality engineer has
taken 15 samples, each containing 200 tires. The total number of defective
tires over the 15 samples is 340. The centerline for the control chart is
a. 0.08
b. 0.11
c. 0.16
d. 0.21
Ans: B, LO: 3, Bloom: K, Difficulty: Easy, AACSB: None
Solution: 340/(15*200)=0.11
70. Consider a production process that produces tires. A quality engineer has
taken 15 samples, each containing 200 tires. The total number of defective
tires over the 15 samples is 340. The sample standard deviation is
a. 0.005
b. 0.011
c. 0.022
d. 0.028
Ans: C, LO: 3, Bloom: K, Difficulty: Easy, AACSB: None
Solution: SQRT(.11*.89/200) = .022
71. Consider a production process that produces tires. A quality engineer has
taken 15 samples, each containing 200 tires. The total number of defective
tires over the 15 samples is 340. The UCL for the control chart constructed
using two sigma is
a. 0.025
b. 0.094
c. 0.122
d. 0.154
Ans: D, LO: 3, Bloom: K, Difficulty: Easy, AACSB: None
Solution: UCL=.11+2*.022=.154
72. Consider a production process that produces tires. A quality engineer has
taken 15 samples, each containing 200 tires. The total number of defective
e.
f.
g.
h.
tires over the 15 samples is 340. The LCL for the control chat constructed
using two sigma is
0.022
0.036
0.048
0.066
Ans: B, LO: 3, Bloom: K, Difficulty: Easy, AACSB: None
Solution: LCL=.11-2*.022=.066
73. Easy Tax is a service company that prepares tax returns. An outside auditor
has examined 20 samples each containing one completed tax return. The total
number of defects observed over the 20 samples is 200. What type of control
chart would you recommend?
a. p-chart
b. c-chart

c. x chart
d. R chart
Ans: B, LO: 3, Bloom: K, Difficulty: Easy, AACSB: None
74. Easy Tax is a service company that prepares tax returns. An outside auditor
has examined 20 samples each containing one completed tax return. The total
number of defects observed over the 20 samples is 200. The centerline for the
control chart constructed is
a. 5
b. 10
c. 15
d. 20
Ans: B, LO:3, Bloom: K, Difficulty: Easy, AACSB: None
Solution: centerline=200/20=10
75. Easy Tax is a service company that prepares tax returns. An outside auditor
has examined 20 samples each containing one completed tax return. The
total number of defects observed over the 20 samples is 200. The standard
deviation for the control chart is
a. 2.2
b. 3.2
c. 3.9
d. 4.5
Ans: B, LO: 3, Bloom: K, Difficulty: Easy, AACSB: None
Solution: standard deviation=Sqrt(10)=3.2
76. Easy Tax is a service company that prepares tax returns. An outside auditor
has examined 20 samples each containing one completed tax return. The
total number of defects observed over the 20 samples is 200. The UCL for the
control chart constructed using three sigma is
a. 19.6
b. 26.7
c. 33.5
d. 50.0
Ans: A, LO: 3, Bloom: K, Difficulty: Easy, AACSB: None
Solution: UCL=10+3*3.2=19.6
77. Easy Tax is a service company that prepares tax returns. An outside auditor
has examined 20 samples each containing one completed tax return. The
total number of defects observed over the 20 samples is 200. The LCL for the
control chart constructed using three sigma is
a. -1.6
b. 0.4
c. 3.3
d. 6.5
Ans: B, LO: 3, Bloom: K, Difficulty: Easy, AACSB: None
Solution: LCL=10-3*3.2=0.4
78. Marble Inc. makes countertops from a variety of high-end materials. To
monitor the quality of its production processes the company randomly selects
one countertop and counts the number of blemishes. The results for ten
samples are shown below:
Sample No.
No. of Blemishes
1
17
2
19
3
15
4
18
5
16
6
14
7
15
8
16
9
15
10
15
Given the sample information above, the average number of defects per unit for
this process would be
a. 160
b. 80
c. 16
d. 10
Ans: C, LO:3, Bloom: K, Difficulty: Moderate, AACSB: None
Solution: average number of defects=(17+19+5+18+16+14+15+16+14+15+15)/10=16
79. Marble Inc. makes countertops from a variety of high-end materials. To
monitor the quality of its production processes the company randomly selects
one countertop and counts the number of blemishes. The results for ten
samples are shown below:
Sample No.
No. of Blemishes
1
17
2
19
3
15
4
18
5
16
6
14
7
15
8
16
9
15
10
15
Given the sample information above, the standard deviation of the number of
defects for this process would be
a. 16
b. 10
c. 4
d. 0
Ans: C, LO: 3, Bloom: K, Difficulty: Moderate, AACSB: None
Solution: Standard deviation=SQRT(16)
80. Marble Inc. makes countertops from a variety of high-end materials. To
monitor the quality of its production processes the company randomly selects
one countertop and counts the number of blemishes. The results for ten
samples are shown below:
Sample No.
No. of Blemishes
1
17
2
19
3
15
4
18
5
16
6
14
7
15
8
16
9
15
10
15
Given the sample information above, the UCL using sigma = 3 for this process
would be
a. 36
b. 32
c. 30
d. 28
Ans: D, LO: 3, Bloom: K, Difficulty: Moderate, AACSB: None
Solution: UCL=16+3*4=28
81. Marble Inc. makes countertops from a variety of high-end materials. To
monitor the quality of its production processes the company randomly selects
one countertop and counts the number of blemishes. The results for ten
samples are shown below:
Sample No.
No. of Blemishes
1
17
2
19
3
15
4
18
5
16
6
14
7
15
8
16
9
15
10
15
Given the sample information above, the LCL using sigma = 3 for this process
would be
a.
b.
c.
d.
12
8
4
0
Ans: D, LO: 3, Bloom: K, Difficulty: Moderate, AACSB: None
Solution: UCL=16-3*4=4
82. A control chart that reflects the amount of variation, or spread, present within
each sample is known as a(n)
a. p-chart
b. c-chart
c. R-chart

d. x -chart
Ans: C, LO: 4, Bloom: K, Difficulty: Easy, AACSB: None
83. Which of the following control charts is used to control the variation within
samples?

a.
b.
c.
d.
x -chart
R chart
c-chart
p-chart
Ans: B, LO: 4, Bloom: K, Difficulty: Moderate, AACSB: None
84. Which of the following control charts is used to control the variation between
samples?

a.
b.
c.
d.
x -chart
R-chart
c-chart
p-chart
Ans: A, LO:4, Bloom: K, Difficulty: Moderate, AACSB: None
85. Which of the following charts are frequently used together to monitor and
control quality?

a.
b.
c.
p and x
R and p
c and R
d.
R and x

Ans: D, LO: 4, Bloom: K, Difficulty: Easy, AACSB: None
86. Pizazz manufactures a 5.0 oz. energy drink of the same name. Because the
cans are so small, consumers are concerned that they are not receiving the full
5 ounces in each can. A quality engineer at the company is charged with
analyzing the filling process and ensuring accurate readings. On 15 different
occasions over the past month, she has taken a sample of 6 energy drinks off
the production line and recorded their weight. If the sum of the sample means
is 80.20 ounces and the sum of the sample ranges is 12.68 ounces, what is the
centerline of an R-chart for this process?
a. .50
b. .85
c. 1.20
d. 1.55
Ans: B, LO: 4, Bloom: K, Difficulty: Easy, AACSB: None
Solution: centerline=12.68/15=.85
87. Pizazz manufactures a 5.0 oz. energy drink of the same name. Because the
cans are so small, consumers are concerned that they are not receiving the full
5 ounces in each can. A quality engineer at the company is charged with
analyzing the filling process and ensuring accurate readings. On 15 different
occasions over the past month, she has taken a sample of 6 energy drinks off
the production line and recorded their weight. If the sum of the sample means
is 80.20 ounces and the sum of the sample ranges is 12.68 ounces, the UCL
for an R-chart of this process would be
a. 0.0
b. 1.0
c. 1.7
d. 2.4
Ans: C, LO: 4, Bloom: K, Difficulty: Easy, AACSB: None
Solution: UCL=2*.85=1.7
88. Pizazz manufactures a 5.0 oz. energy drink of the same name. Because the
cans are so small, consumers are concerned that they are not receiving the full
5 ounces in each can. A quality engineer at the company is charged with
analyzing the filling process and ensuring accurate readings. On 15 different
occasions over the past month, she has taken a sample of 6 energy drinks off
the production line and recorded their weight. If the sum of the sample means
is 80.20 ounces and the sum of the sample ranges is 12.68 ounces, the UCL
for an R-chart of this process would be
a. 0.0
b. 1.0
c. 1.7
d. 2.4
Ans: A, LO: 4, Bloom: K, Difficulty: Easy, AACSB: None
Solution: LCL=0*.85=0.0
89. Pizazz manufactures a 5.0 oz. energy drink of the same name. Because the
cans are so small, consumers are concerned that they are not receiving the full
5 ounces in each can. A quality engineer at the company is charged with
analyzing the filling process and ensuring accurate readings. On 15 different
occasions over the past month, she has taken a sample of 6 energy drinks off
the production line and recorded their weight. If the sum of the sample means
is 80.20 ounces and the sum of the sample ranges is 12.68 ounces, the
centerline for an X-bar chart of this process would be
a. 4.75
b. 5.00
c. 5.35
d. 5.69
Ans: C, LO: 4, Bloom: K, Difficulty: Moderate, AACSB: None
Solution: centerline=80.20/15=5.35
a. 90. Pizazz manufactures a 5.0 oz. energy drink of the same name. Because
the cans are so small, consumers are concerned that they are not receiving the
full 5 ounces in each can. A quality engineer at the company is charged with
analyzing the filling process and ensuring accurate readings. On 15 different
occasions over the past month, she has taken a sample of 6energy drinks off
the production line and recorded their weight. If the sum of the sample means
is 80.20 ounces and the sum of the sample ranges is 12.68 ounces, the UCL
for an X-bar chart of this process would be5.00
b. 5.35
c. 5.76
d. 6.45
Ans: C, LO: 4, Bloom: K, Difficulty: Easy, AACSB: None
Solution: UCL=5.35+.48*.85=5.76
a.
b.
c.
d.
91. Pizazz manufactures a 5.0 oz. energy drink of the same name.
Because the cans are so small, consumers are concerned that they are
not receiving the full 5 ounces in each can. A quality engineer at the
company is charged with analyzing the filling process and ensuring
accurate readings. On 15 different occasions over the past month, she
has taken a sample of 6 energy drinks off the production line and
recorded their weight. If the sum of the sample means is 80.20 ounces
and the sum of the sample ranges is 12.68 ounces, the LCL for an Xbar chart of this process would be
4.50
4.65
4.79
4.94
Ans: D, LO:4, Bloom: K, Difficulty: Easy, AACSB: None
Solution: LCL=5.35-.48*.85=4.94
92. Dumplings –To-Go (DTG) provides take-out dumplings and noodle
dishes to customers at its chain of drive-through restaurants. The target
for a customer’s waiting time is 3.0 minutes +/- 1 minute. Each
month, one of the managers observes the drive-through process and
collects a sample of 4 waiting times a day over a 6 day period. The
data from one restaurant appears below. If DTG were to construct an
X-bar chart from this data, the centerline would be
Samples
1
5.4
2.8
5.7
4.1
2.9
3.3
1
2
3
4
5
6
a.
b.
c.
d.
2
4.6
3.9
3.1
4.3
1.3
4.3
Observations (mins)
3
6.0
4.6
2.8
5.3
4.1
4.2
4
1.5
5.4
2.2
2.8
3.0
3.9
2.87
3.70
3.81
4.28
Ans: C, LO: 4, Bloom: K, Difficulty: Moderate, AACSB: None
Solution: Centerline=(4.38+4.18+3.46+4.13+2.83+3.93)/6 = 3.81
93. Dumplings –To-Go (DTG) provides take-out dumplings and noodle
dishes to customers at its chain of drive-through restaurants. The target
for a customer’s waiting time is 3.0 minutes +/- 1 minute. Each
month, one of the managers observes the drive-through process and
collects a sample of 4 waiting times a day over a 6 day period. The
data from one restaurant appears below. If DTG were to construct an
X-bar chart from this data, the 3-sigma UCL would be
Samples
1
2
3
4
1
5.4
2.8
5.7
4.1
2
4.6
3.9
3.1
4.3
Observations (mins)
3
6.0
4.6
2.8
5.3
4
1.5
5.4
2.2
2.8
5
6
2.9
3.3
a.
b.
c.
d.
1.3
4.3
4.1
4.2
3.0
3.9
6.44
5.87
3.50
2.82
Ans: B, LO: 4, Bloom: K, Difficulty: Moderate, AACSB: None
Solution: UCL =3.81 + .73*2.82 = 5.87
94. Dumplings –To-Go (DTG) provides take-out dumplings and noodle
dishes to customers at its chain of drive-through restaurants. The target
for a customer’s waiting time is 3.0 minutes +/- 1 minute. Each
month, one of the managers observes the drive-through process and
collects a sample of 4 waiting times a day over a 6 day period. The
data from one restaurant appears below. If DTG were to construct an
X-bar chart from this data, the 3-sigma LCL would be
Samples
1
5.4
2.8
5.7
4.1
2.9
3.3
1
2
3
4
5
6
a.
b.
c.
d.
2
4.6
3.9
3.1
4.3
1.3
4.3
Observations (mins)
3
6.0
4.6
2.8
5.3
4.1
4.2
4
1.5
5.4
2.2
2.8
3.0
3.9
0.00
1.00
1.76
2.82
Ans: C, LO: 4, Bloom: K, Difficulty: Moderate, AACSB: None
Solution: LCL=3.81 – (.73*2.82) = 1.76
95. Dumplings –To-Go (DTG) provides take-out dumplings and noodle
dishes to customers at its chain of drive-through restaurants. The target
for a customer’s waiting time is 3.0 minutes +/- 1 minute. Each
month, one of the managers observes the drive-through process and
collects a sample of 4 waiting times a day over a 6 day period. The
data from one restaurant appears below. If DTG were to construct an
R-chart from this data, the centerline would be
Samples
1
5.4
2.8
5.7
4.1
2.9
3.3
1
2
3
4
5
6
a.
b.
c.
d.
2
4.6
3.9
3.1
4.3
1.3
4.3
Observations (mins)
3
6.0
4.6
2.8
5.3
4.1
4.2
4
1.5
5.4
2.2
2.8
3.0
3.9
1.00
2.82
3.54
3.81
Ans: B, LO: 4, Bloom: K, Difficulty: Easy, AACSB: None
Solution: Centerline =(4.5+2.6+3.54+2.5+2.8+1)/6 = 2.82
96. Dumplings –To-Go (DTG) provides take-out dumplings and noodle
dishes to customers at its chain of drive-through restaurants. The target
for a customer’s waiting time is 3.0 minutes +/- 1 minute. Each
month, one of the managers observes the drive-through process and
collects a sample of 4 waiting times a day over a 6 day period. The
data from one restaurant appears below. If DTG were to construct an
R-chart from this data, the 3-sigma UCL would be
Samples
1
5.4
2.8
5.7
4.1
2.9
3.3
1
2
3
4
5
6
a.
b.
c.
d.
2
4.6
3.9
3.1
4.3
1.3
4.3
Observations (mins)
3
6.0
4.6
2.8
5.3
4.1
4.2
4
1.5
5.4
2.2
2.8
3.0
3.9
6.42
5.87
5.63
5.01
Ans: A, LO: 4, Bloom: K, Difficulty: Moderate, AACSB: None
Solution: UCL=2.28 *2.82 = 6.42
97. Dumplings –To-Go (DTG) provides take-out dumplings and noodle
dishes to customers at its chain of drive-through restaurants. The target
for a customer’s waiting time is 3.0 minutes +/- 1 minute. Each
month, one of the managers observes the drive-through process and
collects a sample of 4 waiting times a day over a 6 day period. The
data from one restaurant appears below. If DTG were to construct an
R-chart from this data, the 3-sigma LCL would be
Samples
1
5.4
2.8
5.7
4.1
2.9
3.3
1
2
3
4
5
6
a.
b.
c.
d.
2
4.6
3.9
3.1
4.3
1.3
4.3
Observations (mins)
3
6.0
4.6
2.8
5.3
4.1
4.2
4
1.5
5.4
2.2
2.8
3.0
3.9
2.82
1.41
0.00
-1.41
Ans: C, LO: 4, Bloom: K, Difficulty: Moderate, AACSB: None
Solution: UCL=0 *2.82 = 0
98. Dumplings –To-Go (DTG) provides take-out dumplings and noodle
dishes to customers at its chain of drive-through restaurants. The target
for a customer’s waiting time is 3.0 minutes +/- 1 minute. Each
month, one of the managers observes the drive-through process and
collects a sample of 4 waiting times a day over a 6 day period. The
data for one restaurant appears below. Calculate the process capability
ratio. Is this restaurant capable of meeting DTG standards?
Samples
1
2
3
4
5
6
1
5.4
2.8
5.7
4.1
2.9
3.3
2
4.6
3.9
3.1
4.3
1.3
4.3
Observations (mins)
3
6.0
4.6
2.8
5.3
4.1
4.2
a. yes
b. no
c. Cannot be determined from the above information
Ans: b, LO: 4, Bloom: K, Difficulty: Hard, AACSB: None
Solution: Cp =(4-2)/(5.87-1.76) = .486; No
4
1.5
5.4
2.2
2.8
3.0
3.9
a.
b.
c.
d.
99. In general, a process is considered to be in control for all the following
conditions except
no points are outside the control limits
all points are above the centerline
the points are randomly distributed following a normal population
no pattern exists in the plotted points
Ans: B, LO: 7, Bloom: K, Difficulty: Easy, AACSB: None
100. A process is generally considered to be in control when
a. there are no sample points outside the control limits
b. most points are near the center line, without many being close to the control
limits
c. sample points are randomly distributed equally above and below the center
line
d. All of these answer choices are correct.
Ans: D, LO: 7, Bloom: K, Difficulty: Moderate, AACSB: None
101. For the process to be capable of meeting design specification the process
capability index must be
a. less than one (1.0)
b. equal to or greater than one (1.0)
c. less than zero (0.0)
d. equal to or greater than zero (0.0)
Ans: B, LO: 7, Bloom: K, Difficulty: Moderate, AACSB: None
a. 102. A company produces a product which is designed to weigh 10 oz., with a
tolerance of + 0.5 oz. The process produces products with an average weight
of 9.95 oz. and a standard deviation of 0.10 oz. The process capability ratio
for this process is 1.67
b. 0
c. 0.8333
d. -1.67
Ans: A, LO: 7, Bloom: K, Difficulty: Hard, AACSB: None
Solution: process capability ratio=1.0/(6*0.1)=1.67
103. A company produces a product which is designed to weigh 10 oz., with a
tolerance of + 0.5 oz. The process produces products with an average weight of
9.95 oz. and a standard deviation of 0.10 oz. According to the process capability
ratio is the process capable of meeting design specifications?
a. No, the process capability ratio is less than 1.0
b. Yes, the process capability ratio is less than 1.0
c. No, the process capability ratio is greater than 1.0
d. Yes, the process capability ratio is greater than 1.0
Ans: D, LO: 7, Bloom: K, Difficulty: Hard, AACSB: None
Solution: process capability ratio=1.0/(6*0.1)=1.67
104. A company produces a product which is designed to weigh 10 oz., with a
tolerance of + 0.5 oz. The process produces products with an average weight of
9.95 oz. and a standard deviation of 0.10 oz. The process capability index for this
process is
a. 1.50
b. -1.50
c. 1.83
d. -1.83
Ans: A, LO: 7, Bloom: K, Difficulty: Hard, AACSB: None
Solution: Process capability index=min{(.55/(3*.1),(45/(3*.1)}=min{1.83,1.50}=1.50
105. A company produces a product which is designed to weigh 10 oz., with a
tolerance of + 0.5 oz. The process produces products with an average weight of
9.95 oz. and a standard deviation of 0.10 oz. According to the process capability
index
a. the process mean is off center having shifted to the right
b. the process mean is off center having shifted to the left
c. the process mean is centered on the design target
d. None of these answer choices is correct.
Ans: A, LO: 7, Bloom: K, Difficulty: Hard, AACSB: None
Solution: Process capability index=min{(.55/(3*.1),(45/(3*.1)}=min{1.83,1.50}=1.50
a.
b.
c.
d.
106.XYZ manufacturing has received an order to produce a rod 5 inches
in diameter + .04 inch. In sample runs, the machine tool that will be
making the rod has been able to produce rods with a mean diameter of
4.99 inches and a standard deviation of 0.011 inch. The process
capability ratio for this process is
-1.44
-1.21
1.21
1.44
Ans: C, LO: 7, Bloom: K, Difficulty: Hard, AACSB: None
Solution: process capability ratio=0.08/(6*.011)=1.21
107. XYZ manufacturing has received an order to produce a rod 5 inches
in diameter + .04 inch. In sample runs, the machine tool that will be
making the rod has been able to produce rods with a mean diameter of
4.99 inches and a standard deviation of 0.011 inch. The process
capability index for this process is
a.
b.
c.
d.
0.91
1.51
-0.91
-1.51
Ans: A, LO:7, Bloom: K, Difficulty: Hard, AACSB: None
Solution: process capability index=min{0.03/(3*.011),(0.05/(3*.011)}=min{0.91,1.51}=1.5
108.XYZ manufacturing has received an order to produce a rod 5 inches
in diameter + .04 inch. In sample runs, the machine tool that will be
making the rod has been able to produce rods with a mean diameter of
4.99 inches and a standard deviation of 0.011 inch. Which of the
following statements is true?
a. The process is capable of meeting design spec but is off-center.
b. The process is capable of meeting design specs and is on-center.
c. The process in incapable of meeting design specs.
Ans: C, LO: 7, Bloom: K, Difficulty: Hard, AACSB: None
Solution: Cp <1, so incapable.
Short Answer Questions
109.
Briefly discuss attribute and variable quality measures.
Ans: Essay, LO: 2, Bloom: K, Difficulty: Hard, AACSB: None
Solution:
The quality of a product or service can be evaluated using either an
attribute of the product or service or a variable measure. An attribute is a
product characteristic such as color, surface texture, or perhaps smell or
taste. Attributes can be evaluated quickly with a discrete response such as
good or bad, acceptable or unacceptable, or yes or no. Even if quality
specifications are complex and extensive, a simple attribute test might be
used to determine if a product or service is or is not defective. A variable
measure is a product characteristic that is measured on a continuous scale
such as length, width, time, or temperature. Because a variable evaluation
is the result of a measurement it is sometimes referred to as a quantitative
classification method. An attribute evaluation is sometimes referred to as a
qualitative classification, since the response is not measured. Because it is
a measurement, a variable typically provides more information about the
product that does an attribute.
110.Using control charts, how do we evaluate whether a process is in
control?
Ans: Essay, LO:2, Bloom: K, Difficulty: Hard, AACSB: None
Solution:
Sample points are plotted on the control chart and the chart is examined to
determine if the process is in control. Generally, a process will be
considered to be in control if (a) there are no sample points outside the
control limits, (b) most points are near the process average or center line,
without too many close to the control limits, (c) approximately equal
numbers of sample points occur above and below the center line, and (d)
the points appear to be randomly distributed around the center line. If any
of these conditions are violated, the process may be out of control.
111.
What is a c-chart and when is it used?
Ans: Essay, LO: 3, Bloom: K, Difficulty: Hard, AACSB: None
Solution:
A c-chart is a type of attribute control chart. A c-chart uses the actual
number of defects per item in a sample. A c-chart is used when it is not
possible to compute a proportion defective and the actual number of
defects must then be used. For example, it is possible to count the number
of blemishes on a painted surface but we cannot compute a proportion
because the total number of possible blemishes is not known. In such a
situation the number of blemishes would be monitored using a c-chart.
_
112.
Why are x and R-charts used together?
Ans: Essay, LO: 4, Bloom: K, Difficulty: Hard, AACSB: None
Solution:
When monitoring a variables characteristic, that is one that can be
measured, it is possible for the process to lose control in terms of its
central tendency (mean) and in terms of its variability (range). IN order for
the process to be in control it must be in control with respect to its average
and its variability. The two charts measure the process differently. It is
possible for samples to have very narrow ranges, suggesting little process
variability, but the sample averages might be beyond the control limits.
Conversely, it is possible for sample averages to be in control, but the
ranges might be very large. IN order to monitor both the mean and the
variability of a process using a variable measured on a continuous scale
the two charts must be used together.
113.
What is the process capability ratio and how is
Ans: Essay, LO: 7, Bloom: K, Difficulty: Hard, AACSB: None
it calculated?
Solution:
Process capability refers to the natural variation of a process relative to the
variation allowed by the design specifications. In other words, how
capable is the process of producing acceptable units according to the
design specifications? Process control charts are used for process
capability to determine if an existing process is capable of meeting design
specifications. There are three main elements associated with process
capability—process variability (the natural range of variation of the
process), the process center line (mean), and the design specifications.