Introduction to Reliability Analysis pp 44-66 | Cite as

# Reliability of Composite Systems

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## Abstract

In the present chapter we discuss methods of determining the reliability of a system when we have information on the reliability of its subsystems, or components, and we know the structure of the system. The reliability function is a function of time, *R* (*t*), 0 < *t* < ∞. In much of the discussion the time argument, *t*, is fixed at a given value, say t_{0}. Thus, we can often suppress the time variable and write *R* for *R*(*t*_{0}). Furthermore, if a system is comprised of n subsystems (components), the corresponding reliability values will be denoted by *R* _{1}, *R*_{2}, ···, *R*_{ n }. The reliability of the whole system will be denoted by *R* _{ sys }. We would like to be able to express the reliability of the system, *R* _{ sys }, as a function *ψ*(*R* _{1}, ···, *R* _{ n }, of the reliability values of its subsystems. This is generally possible if one has a well defined structure function which describes the interrelations among the subsystems, and if the failure times of the subsystems are mutually independent random variables. If the failure times are not independent but correlated, it may be impossible to determine *R*_{ sys } just from the information on *R* _{1} ···, *R* _{ n } One may need some further information. In such cases, however, upper and lower bounds for *R* _{ sys } can often be determined as functions of *R* _{1}, ···, *R* _{ n }.

## Keywords

Block Diagram Failure Probability Failure Time System Reliability Fault Tree## Preview

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