THE NOTION OF COMPOSITE RELIABILITY AND ITS HIERARCHICAL BAYES ESTIMATION

In this article we introduce the notion of ''composite reliability'' a s a measure of the overall reliability of a collection of heterogeneou s but similar items. We then propose a hierarchical Bayes model for es timating the composite reliability of systems whose lifelengths are ex pressed as binary random variables. Subsequently, we develop an altern ative approach for the simultaneous inference about many small but rel ated binomial parameters. We propose a two-stage prior for addressing problems of this type and use the Gibbs sampler algorithm for addressi ng problems involving small proportions. Our topic, though suggested b y an issue pertaining to the safety of nuclear power plants, arises in other commonly occurring situations pertaining to consumerism, public policy, and government regulation. Our development generalizes for si tuations involving lifelengths that need not be binary.