Management

Reliability

LEARNING OBJECTIVES

After completing this supplement,

you should be able to:

1 Define reliability.

2 Perform simple reliability

computations.

3 Explain the purpose of redundancy

in a system.

Finding the Probability of Functioning When Activated

The probability that a system or a product will operate as planned is an important concept in

system and product design. Determining that probability when the product or system consists

of a number of independent components requires the use of the rules of probability for independent

events. Independent events have no relation to the occurrence or nonoccurrence of

each other. What follows are three examples illustrating the use of probability rules to determine

whether a given system will operate successfully.

Rule 1. If two or more events are independent and success is defined as the probability that

all of the events occur, then the probability of success is equal to the product of the probabilities

of the events.

Example Suppose a room has two lamps, but to have adequate light both lamps must work

(success) when turned on. One lamp has a probability of working of .90, and the other has

a probability of working of .80. The probability that both will work is .90 _ .80 _ .72. Note

that the order of multiplication is unimportant: .80 _ .90 _ .72. Also note that if the room

had three lamps, three probabilities would have been multiplied.

This system can be represented by the following diagram:

.90 .80

Lamp 1 Lamp 2

Even though the individual components of a system might have high reliabilities, the system

as a whole can have considerably less reliability because all components that are in series

(as are the ones in the preceding example) must function. As the number of components in a

series increases, the system reliability decreases. For example, a system that has eight components

in a series, each with a reliability of .99, has a reliability of only .99 8 _ .923.

Obviously, many...