Bayesian Analysis of Reliability in Multicomponent Stress-Strength Models.

This paper provides a Bayesian treatment of the problem of inference about the reliability of a multicomponent stress-strength system which functions if s or more of k identical components simultaneously operate. All stresses and strengths are assumed to be independent, exponentially distributed random variables. Exact and approximate asymptotic posterior distributions for the reliability are derived, and the various results are illustrated by numerical examples. Typically, components are mass produced and a sample of strengths can be generated from laboratory load tests on a random sample of the components. Also, the data of stress can be obtained from a simulation of conditions for operating the system. Thus, such data may be used for inference on the reliability of any s out of k system. It is not necessary to construct and test a complete system for each contemplated choice of s and k.