Using the negative log-gamma distribution for Bayesian system reliability assessment

Abstract

Modeling system reliability over time when binary data are collected both at the system and component level has been the subject of many papers. In a series system, it is often assumed that component reliability is linear in time through some link function. Often little or no information exists on the parameters of the linear regression, and in a Bayesian analysis they are modeled using diffuse priors. This can have unintended consequences for the analysis, specifically for the extrapolation of component and system reliabilities. In this work, we consider negative log-gamma (NLG) distributions for specifying prior information on reliability. We first show how our method can be implemented to model the reliability of a series system at a given time and extend to the case where we are interested in modeling reliability over time. We then discuss methods of estimation for the parameters of the NLG prior based on quantiles obtained from expert knowledge. Finally, we propose a component selection approach to help identify active and inactive components. The component selection approach leads to reasonable estimates of trend in the reliability of a large system when only a few components among many actually contribute to the trend.