A Bayesian approach to prediction of system failure rates by criticalities under event trees

Abstract

A Bayesian approach under a binary multi-stage event tree is proposed in estimating the system failure rate in various levels of criticality in order to incorporate failure data in one level into analyzing failure rates in any other levels. An initial failure which occurs according to a Poisson process with unknown rate is to escalate to more severe failures depending on functioning states of backup subsystems associated with the event tree. We employ the Gamma prior distribution for the initial failure rate and the Beta priors for the criticality probabilities. An approximation method is proposed to obtain the posterior distributions of the failure rates by criticalities. (C) 1999 Elsevier Science B.V. All rights reserved.