Bayesian Reliability Analysis of High-Reliability Systems of Binomial and Poisson Subsystems

A Bayesian procedure for estimating the reliability of a complex system of independent series and parallel subsystems is presented. This method accepts either binomial or Poisson test data (perhaps both or neither) as inputs, as well as prior information, at any and all levels in the system (such as the component, subsystem and system levels). Natural conjugate beta and gamma priors are considered. A numerical example concerning the unreliability of the low-pressure coolant injection system of a certain U.S. commercial nuclear-powered boiling water reactor is used to illustrate the procedure. A Mathematica^® notebook is available for implementing the method.