Reliability of Composite Systems

  • Shelemyahu Zacks
Part of the Springer Texts in Statistics book series (STS)


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 t0. Thus, we can often suppress the time variable and write R for R(t0). Furthermore, if a system is comprised of n subsystems (components), the corresponding reliability values will be denoted by R 1, R2, ···, 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 .


Block Diagram Failure Probability Failure Time System Reliability Fault Tree 
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Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • Shelemyahu Zacks
    • 1
  1. 1.Department of Mathematical SciencesState University of New York at BinghamtonBinghamtonUSA

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