Use the following table to answer the question(s) below.
Bench #
1
2
3
4
5
6
7
8
9
10
# Drips
9
10
3
4
4
11
14
13
11
13
51) A parks and recreation worker counts the number of paint drips on each standard size park
bench. The results from the last 10 benches are shown.
If the Parks Department decides to make a c chart, what should the center line be?
A) 6.9
B) 8.4
C) 9.2
D) 10.7
E) 11.3
52) A parks and recreation worker counts the number of paint drips on each standard size park
bench. The results from the last 10 benches are shown.
If the Parks Department decides to make a c chart, what should the lower and upper 3-sigma
control limits be?
A) (-9.2, 9.2)
B) (0.0, 20)
C) (0.1, 18.3)
D) (3.1, 13.1)
E) (3.1, 18.3)
53) What is a np chart and how is it similar to or different than a p chart?
54) What is a u chart and how is it similar to or different than a c chart?
55) The reliability model that shows that products are more likely to fail either very early in their
useful life or very late in their useful life is called the ________.
A) half-moon hazard function
B) saucer-shaped hazard function
C) half-circle hazard function
D) cone-shaped hazard function
E) bathtub-shaped hazard function
56) The vertical axis on the bathtub function is ________.
A) failure rate
B) time
C) predicted life
D) design reliability
E) useful life
57) The horizontal axis on the bathtub function is ________.
A) failure rate
B) time
C) useful life
D) design reliability
E) predicted life
58) Reliability models assume statistical independence between failure events. This means that
________.
A) components do not fail
B) if one component fails, the entire system fails
C) parallel systems are unnecessary
D) the failure of one component does not influence another to fail
E) series systems are unnecessary
59) System unreliability is increased with ________.
A) a redundant system
B) a parallel system
C) a backup system
D) high reliability components
E) low reliability components
60) A system is composed of three components. Two of the items are in parallel and have
reliabilities of 0.95 and 0.90. The third item has a reliability of 0.98 and this item is in series with
the first combination. What is the overall system reliability?
A) 0.995
B) 0.985
C) 0.975
D) 0.965
E) 0.955
61) A system is composed of three components in series having reliabilities of 0.99, 0.95, and
0.90. What is the overall system reliability?
A) 0.95
B) 0.90
C) 0.85
D) 0.80
E) 0.75
62) A system is composed of three components in series having reliabilities of 0.85, 0.92, and
0.90. What is the overall system reliability?
A) 0.90
B) 0.85
C) 0.80
D) 0.75
E) 0.70
63) A system is composed of three components in series having reliabilities of 0.99, 0.98, and
0.97. What is the overall system reliability?
A) 0.97
B) 0.96
C) 0.95
D) 0.94
E) 0.93
64) A system is to be composed of 5 identical components in series. What is the lowest reliability
component that can be used in order to have an overall system reliability of 0.90?
A) 0.98
B) 0.97
C) 0.96
D) 0.95
E) 0.94
65) A system is to be composed of 10 identical components in series. What is the lowest
reliability component that can be used in order to have an overall system reliability of 0.90?
A) 0.99
B) 0.98
C) 0.97
D) 0.96
E) 0.95
66) A system is to be composed of 4 identical components in series. What is the lowest reliability
component that can be used in order to have an overall system reliability of 0.85?
A) 0.93
B) 0.94
C) 0.95
D) 0.96
E) 0.97
67) Two components of reliability 0.90 are in parallel and this subsystem is connected in series
to a component with a reliability of 0.95. The overall system reliability is ________.
A) 0.93
B) 0.94
C) 0.95
D) 0.96
E) 0.97
68) Two components of reliability 0.95 are in parallel and this subsystem is connected in series
to a component with a reliability of 0.90. The overall system reliability is ________.
A) 0.82
B) 0.84
C) 0.86
D) 0.88
E) 0.90
69) Two components of reliability 0.95 are in parallel and this subsystem is connected in series
to a component with a reliability of 0.95. The overall system reliability is ________.
A) 0.93
B) 0.94
C) 0.95
D) 0.96
E) 0.97
70) Fifty defibrillators are tested for 48 hours per machine. Of all the machines tested, 2
experience malfunctions during the test. What is the failure rate for the machines?
A) 0.004
B) 0.042
C) 0.01
D) 0.008
E) 0.0008
71) Fifty crash helmets are tested for one hundred hours per helmet. Of all the helmets tested,
only one experiences a malfunction during the test. What is the failure rate for the helmets?
A) 0.0002
B) 0.002
C) 0.004
D) 0.0008
E) 0.016
72) What is the reliability of a product with a failure rate of 0.002 per operating hour and a useful
life of 1000 hours?
A) 0.14
B) 0.22
C) 0.50
D) 0.78
E) 0.86
73) What is the reliability of a product with a failure rate of 0.001 per operating hour and a useful
life of 1500 hours?
A) 0.14
B) 0.22
C) 0.50
D) 0.78
E) 0.86
74) What is the reliability of a product with a failure rate of 0.015 per operating hour and a useful
life of 250 hours?
A) 0.14
B) 0.12
C) 0.88
D) 0.98
E) 0.02
75) What is the useful life in hours for a product having a reliability of 0.999 and a failure rate of
0.015 failures per hour?
A) 400
B) 420
C) 440
D) 460
E) 480
76) What is the approximate useful life in hours for a product having a reliability of 0.9978 and a
failure rate of 0.001 failures per hour?
A) 6120
B) 5600
C) 5000
D) 4400
E) 3800
77) What is the useful life in hours for a product having a reliability of 0.985 and a failure rate of
0.015 failures per hour?
A) 120
B) 200
C) 280
D) 360
E) 440
78) What is the system availability for something that has a mean time between failures of 50
hours and needs an average of 1 hour to repair when it does fail?
A) 0.98
B) 0.92
C) 0.86
D) 0.80
E) 0.74
79) What is the system availability for something that has a mean time between failures of 100
hours and needs an average of 4 hours to repair when it does fail?
A) 0.98
B) 0.92
C) 0.96
D) 0.90
E) 0.84
80) What is the system availability for something that has a mean time between failures of 168
hours and needs an average of 48 hours to repair when it does fail?
A) 0.98
B) 0.93
C) 0.88
D) 0.83
E) 0.78
81) A system has an availability of 90% and a mean time to repair of 48 hours. What is the mean
time between failures?
A) 400 hours
B) 432 hours
C) 464 hours
D) 496 hours
E) 528 hours
82) A local university is deciding between three different copy machines. The copy machines
have a mean time between failure and mean time to repair as shown in the table.
MTBF
MTTR
Copier A
48 hours
1 hour
Copier B
168 hours
5 hours
Copier C
300 hours
8 hours
What system(s) will provide the greatest availability?
A) Copier A
B) Copier B
C) Copier C
D) Copier A and Copier B
E) Copier B and Copier C
83) A local fraternity is deciding between three different refrigerators. The refrigerators have a
mean time between failure and mean time to repair as shown in the table.
MTBF
MTTR
Refrigerator A
50 hours
2 hours
Refrigerator B
125 hours
3 hours
Refrigerator C
200 hours
4 hours
What refrigerator(s) will provide the greatest availability?
A) Refrigerator A
B) Refrigerator B
C) Refrigerator C
D) Refrigerator A and Refrigerator B
E) Refrigerator A and Refrigerator C
84) A local university is deciding between three different computer networks. The network
servers have a mean time between failure and mean time to repair as shown in the table.
MTBF
MTTR
Server A
100 hours
1 hour
Server B
250 hours
2 hours
Server C
400 hours
3 hours
Which server(s) will provide the greatest availability?
A) Server A
B) Server B
C) Server C
D) Server A and Server B
E) Server B and Server C
85) The vertical axis on the bathtub curve is failure rate.
86) The horizontal axis on the bathtub curve is reliability.
87) Components in a system are in parallel if the performance of the entire system depends on all
its components functioning properly.
88) Reliability models assume independence between failure events.
89) Three items of reliability 0.90 in series has an overall system reliability of 0.73.
90) One item with a reliability of .95, followed by two items in parallel having a reliability of
0.90, have an overall system reliability of 0.94.
91) When testing failure rate, there is no distinction as to whether hours of testing are continuous
or performed at separate times.
92) One way to achieve very high system availability would be for the mean time between
failures to be as low as possible.
93) One way to raise system availability would be to lower the mean time to repair.
94) The reliability of a product having a failure rate of 0.0001 and a useful life of 2080 hours is
0.81.
95) The object of using process charts is to continually improve your processes.
96) In order to determine system availability, you will need both the mean time to failure and the
mean time between failures.
97) The mean time between failures is the average time before the product will fail.
98) If a set of components is in a series, as opposed to being parallel, the system can function if a
given component in the system fails.
99) Describe the development and interpretation of the bathtub curve.
100) Discuss series and parallel reliability models and the implications for product design.
101) The reliability of components in series is the product of their individual reliabilities. What
implications does this have for the Space Shuttle?