Bayesian Confidence Limits for the Reliability of Mixed Cascade and Parallel Independent Exponential Subsystems

This paper deals with the theoretical problem of derving Bayesian confidence intervals for the reliability of a system consisting of both cascade and parallel subsystems where each subsystem is independent and has an exponential failure probability density function (pdf). This approach is applicable when test data are available for each individual subsystem and not for the enfire system. The Mellin integral transform is used to analyze the system in a step-by-step procedure until the posterior pdf of the system reliability is obtained. The posterior cumulative distribution function is then obtained in the usual manner by integrating the pdf, which serves the dual purpose of yielding system reliability confidence limits while at the same time providing a check on the accuracy of the derived pdf. A computer program has been written in FORTRAN IV to evaluate the confidence limits. An example is presented which uses the computer program.