Bayesian Estimation of Component Reliability in Coherent Systems

The first step in statistical reliability studies of coherent systems is the estimation of the reliability of each system component. For the cases of parallel and series systems, the literature is abundant, but it seems that the present paper is the first to present the general case of component inferences in coherent systems. The failure time model considered here is the three-parameter Weibull distribution. Furthermore, identically distributed failure times are not a required restriction. An important result is proved: without the assumption that components' lifetimes are mutually independent, a given set of sub-reliability functions does not identify the corresponding marginal reliability function. The proposed model is general in the sense that it can be used for components of any coherent system, from the simplest to the most complex designs. It can be considered for all kinds of censored data, including interval-censored data. An important property obtained for the Weibull model is that the posterior distributions are proper, even for non-informative priors. Using several simulations, the excellent performance of the model is illustrated. As real examples, boys' first use of marijuana and a device from a field-tracking data set are considered to show the efficiency of the solution even when censored data occurs.