RELIABILITY:SYSTEM RELIABILITY

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SYSTEM RELIABILITY

The structure function of a system containing n components is a binary random variable that takes on the value 1 or 0. Furthermore, the reliability of this system can be expressed as2

INTRODUCTION TO OPERATIONS RESEARCH-0608

1It is evident that the loss of the front or rear brakes will affect the braking capability of the automobile, but the definition of “perform successfully” may allow for either set working.

2The time t is now suppressed in the notation. Recall that the time is implicitly included in determining whether or not the ith component performs satisfactorily.

In general, such conditional probabilities require careful analysis. For example, P{X2 = 1½X1 = 1} is the probability that component 2 will perform successfully, given that component 1 performs successfully. Consider a system where the heat from component 1 affects the temperature of component 2 and thereby its probability of success. The performance of these components is then dependent, and the evaluation of the conditional probability is extremely difficult. If, on the other hand, the performance characteristics of these components do not interact, e.g., the temperature of one component does not affect the performance of the other component, then the components can be said to be independent. The expression for the reliability then simplifies and becomes

INTRODUCTION TO OPERATIONS RESEARCH-0609

INTRODUCTION TO OPERATIONS RESEARCH-0610

This result is analogous to, and dependent upon, the assumption that the structure function of the system is coherent. The implication of this intuitive result is that the reliability of the automobile will improve if the reliability of one or more components is improved.

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