A computerized solution technique for the analysis of generalized, Bayesian, distribution-free reliability networks utilizing pass-fail data from the component level

Abstract

A solution technique for the analysis of generalized, distribution-free reliability networks is developed. It is applicable to systems consisting of independent cascade and/or parallel subsystems for which component pass-fail data are available. No assumption is made concerning the distribution of each component's life density function, except that it is continuous. Bayesian probability techniques utilizing the Mellin integral transform are applied to analyze system reliability. An approximation to the posterior density function of system reliability is generated, from which arbitrary Bayesian confidence limits may be readily obtained by means of numerical integration. The approximation to the posterior density function is based upon exact moments of system reliability obtained from the relevant Mellin transforms. The developed solution techniques are incorporated into a computerized model that decomposes and suitably analyzes any generalized system. The computer model requires data that may be taken directly from a reliability block diagram. It calculates the mean and variance of each component's reliability, the theoretically exact moments and variance and approximate desired confidence limits of system reliability. Analysis of reliability systems for which closed form solutions exist is used for validation of the developed computerized model. In addition, the usefulness of the model is demonstrated by analyzing more complex network configurations that do not lend themselves to closed form solutions.