Operations management by stevenson 9th ch4s

4S

Reliability

McGraw-Hill/Irwin

Copyright © 2007 by The McGraw-Hill Companies, Inc. All


Learning Objectives
 Define reliability
 Perform reliability computations
 Explain the purpose of redundancy in a
system

4S-2


Reliability
 Reliability: The ability of a product, part,

or system to perform its intended function
under a prescribed set of conditions

 Failure: Situation in which a product,
part, or system does not perform as
intended

 Normal operating conditions: The set
of conditions under which an item’s
reliability is specified

4S-3


Reliability is a Probability
 Probability that the product or system will:
 Function when activated
 Function for a given length of time

 Independent events
 Events whose occurrence or nonoccurrence
do not influence each other

 Redundancy
 The use of backup components to increase
reliability

4S-4


Rule 1

Lamp 1

.90

Lamp 2

.80

.90 x .80 = .72

4S-5


Rule 2

.80

Lamp 2 (backup)

.90 + (1-.90)*.80 = .98

.90
Lamp 1

4S-6


Rule 3
.70

.80

.90

Lamp 3 (backup for Lamp 2)

Lamp 2 (backup for Lamp1)

1 – P(all fail)
1-[(1-.90)*(1-.80)*(1-.70)] = .994
Lamp 1

4S-7


Example S-1 Reliability
Determine the reliability of the system shown

.98

.90

.92

.90

.95

4S-8


Example S-1 Solution
The system can be reduced to a series of three
components

.98

.90+.90(1-.90)

.95+.92(1-.95)

.98 x .99 x .996 = .966

4S-9


Failure Rate

Failure Rate

Figure 4S.1

Infant
mortality

Failures due
Few (random) failures
to wear-out
Time, T

4S-10


Exponential Distribution

Figure 4S.2

Reliability = e -T/MTBF

1- e -T/MTBF
T

Time

4S-11


Normal Distribution
Figure 4S.3

Reliability

0

z

4S-12


Availability
 The fraction of time a piece of equipment
is expected to be available for operation
Availability 

MTBF
MTBF  MTR

MTBF = mean time between failures
MTR = mean time to repair

4S-13


Improving Reliability








Component design
Production/assembly techniques
Testing
Redundancy/backups
Preventive maintenance procedures
User education
System design

4S-14