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17
C H A P T E R
Maintenance and Reliability
1. The objective of maintenance and reliability is to maintain the
capability of the system while controlling costs.
2. Candidates for preventive maintenance can be identified
by looking at the distributions for MTBF (mean time between
failures). If the distributions have a small standard deviation, they
4. Simulation is an appropriate technique with which to investi-
gate maintenance problems because failures tend to occur ran-
domly, and the probability of occurrence is often described by a
6. Some ways in which the manager can evaluate the effective-
ness of the maintenance function include:
◼ Maintenance productivity as measured by:
Units of production
Emergency maintenance hours
1Preventative maintenance hours
−
7. Machine design can ameliorate the maintenance problem by,
among other actions, stressing component reliability, simplicity of
design and the use of common or standard components, simplicity
8. Information technology can play a number of roles in the
maintenance function, among them:
◼ Files of parts and vendors
◼ Active monitoring of system states
9. The best response would probably be to enumerate the actual
costs, both tangible and intangible, for each practice.
Costs of waiting until it breaks to fix it might include:
260 CHAPTER 17 MAINT ENA NC E AN D RE L IAB IL IT Y
ETHICAL DILEMMA
Yes, as the man said: “You can be perfectly safe and never get off
1. Would it be better to increase the worst clerk’s reliability
from .8 to .81 or the best clerk’s reliability from .99 to 1?
Increase the worst clerk’s reliability from .8 to .81.
2. Is it possible to achieve 90% reliability by focusing on only
one of the three clerks?
No—the best we can do is 89.1% reliability, even with R2
to 100%.
ACTIVE MODEL 17.2: Redundancy
1. If one additional clerk were available, which would be the
best place to add this clerk as back-up?
At R2, yielding a system reliability of 97.23%.
2. What is the minimum number of total clerks that need to be
added as backup in order to achieve a system reliability of 99%?
Three more clerks—one more at each process.
are used?
With the middle pair of components set to 0.0, reliability
4. What is the reliability if components 2 and 3 have reliability
of only .95?
With the reliability of the middle pair set to .95 (all at .95),
6. Suppose that components 2 and 3 both must have the same
reliability. What does that need to be in order to have an overall
reliability of .9999?
17.5 Let R equal the reliability of the components. Then
R1 R2 R3 = Rs, the reliability of the overall system. Therefore,
R3 = 0.98 and each R 0.9933. Therefore, a reliability of
approximately 99.33% is required of each component.
17.6 (a) Percent of failures [FR(%)]
( )
5
% 0.05 5.0%
100
F= = =
(b) Number of failures per unit hour [(FR(N)]:
( )
Number of failures
Total time Nonoperating time
FR N =−
where
Total time = (5,000 hrs) (100 units)
= 500,000 unit-hours
Non-operating time = (2,500 hrs) (5 units) = 12,500
55
17.7 (a)
( )
4
% 40%
10
FR ==
(b)
FR N
= − +
+
( ) 4 (10 60,000) (50,000 1) (35,000 1)
(15,000 2)
CHAPTER 17 MAINTENANCE AND REL I AB ILI T Y 261
17.8 The overall system has a reliability of 0.9941, or approxi-
mately 99.4%.
17.9 The overall system has a reliability of 0.9498, or approxi-
mately 95%.
17.15 The figure suggests that there are likely to be at least three
separate modes of failure; one or more causes of infant mortality,
and two modes of failure which occur at later times.
17.16
(a) With a backup reliability of 0.90:
{0.90 [0.90(1 0.90)]} {0.92 [0.90(1 0.92)]}
{0.94 [0.90(1 0.94)]} {0.96 [0.90(1 0.96)]}
{0.90 0.90 0.10} {0.92 0.90 0.08}
{0.94 0.90 0.06} {0.96 0.90 0.04}
{0.900 0.090} {0.920 0.072}
{0.940 0.054}
R= + − + −
+ + − + + −
= + +
+ +
= + +
+ {0.960 0.036}
0.972
+
=
Reliability Probability Probability Probability
of a of first of backup of needing
= + ×
system with component component backup
a backup working working component
262 CHAPTER 17 MAINT ENA NC E AN D RE L IAB IL IT Y
( )
Number of failures
Total time non-operating time
FR N =−
where:
Total time (4,000 hr.) (200 units)
=
1. What might be done to help take Frito-Lay to the next level of
outstanding maintenance? Consider factors such as sophisticated
software.
Frito-Lay’s Florida plant is establishing a world-class
260 CHAPTER 17 MAINT ENA NC E AN D RE L IAB IL IT Y
ETHICAL DILEMMA
Yes, as the man said: “You can be perfectly safe and never get off
1. Would it be better to increase the worst clerk’s reliability
from .8 to .81 or the best clerk’s reliability from .99 to 1?
Increase the worst clerk’s reliability from .8 to .81.
2. Is it possible to achieve 90% reliability by focusing on only
one of the three clerks?
No—the best we can do is 89.1% reliability, even with R2
to 100%.
ACTIVE MODEL 17.2: Redundancy
1. If one additional clerk were available, which would be the
best place to add this clerk as back-up?
At R2, yielding a system reliability of 97.23%.
2. What is the minimum number of total clerks that need to be
added as backup in order to achieve a system reliability of 99%?
Three more clerks—one more at each process.
are used?
With the middle pair of components set to 0.0, reliability
4. What is the reliability if components 2 and 3 have reliability
of only .95?
With the reliability of the middle pair set to .95 (all at .95),
6. Suppose that components 2 and 3 both must have the same
reliability. What does that need to be in order to have an overall
reliability of .9999?
17.5 Let R equal the reliability of the components. Then
R1 R2 R3 = Rs, the reliability of the overall system. Therefore,
R3 = 0.98 and each R 0.9933. Therefore, a reliability of
approximately 99.33% is required of each component.
17.6 (a) Percent of failures [FR(%)]
( )
5
% 0.05 5.0%
100
F= = =
(b) Number of failures per unit hour [(FR(N)]:
( )
Number of failures
Total time Nonoperating time
FR N =−
where
Total time = (5,000 hrs) (100 units)
= 500,000 unit-hours
Non-operating time = (2,500 hrs) (5 units) = 12,500
55
17.7 (a)
( )
4
% 40%
10
FR ==
(b)
FR N
= − +
+
( ) 4 (10 60,000) (50,000 1) (35,000 1)
(15,000 2)
CHAPTER 17 MAINTENANCE AND REL I AB ILI T Y 261
17.8 The overall system has a reliability of 0.9941, or approxi-
mately 99.4%.
17.9 The overall system has a reliability of 0.9498, or approxi-
mately 95%.
17.15 The figure suggests that there are likely to be at least three
separate modes of failure; one or more causes of infant mortality,
and two modes of failure which occur at later times.
17.16
(a) With a backup reliability of 0.90:
{0.90 [0.90(1 0.90)]} {0.92 [0.90(1 0.92)]}
{0.94 [0.90(1 0.94)]} {0.96 [0.90(1 0.96)]}
{0.90 0.90 0.10} {0.92 0.90 0.08}
{0.94 0.90 0.06} {0.96 0.90 0.04}
{0.900 0.090} {0.920 0.072}
{0.940 0.054}
R= + − + −
+ + − + + −
= + +
+ +
= + +
+ {0.960 0.036}
0.972
+
=
Reliability Probability Probability Probability
of a of first of backup of needing
= + ×
system with component component backup
a backup working working component
262 CHAPTER 17 MAINT ENA NC E AN D RE L IAB IL IT Y
( )
Number of failures
Total time non-operating time
FR N =−
where:
Total time (4,000 hr.) (200 units)
=
1. What might be done to help take Frito-Lay to the next level of
outstanding maintenance? Consider factors such as sophisticated
software.
Frito-Lay’s Florida plant is establishing a world-class
