Estimation of Component Reliability in Coherent Systems

TL;DR

This paper introduces a comprehensive Bayesian method for estimating component reliabilities in any coherent system using Weibull failure models, accommodating complex structures and various censored data types.

Contribution

It presents the first general Bayesian approach for component inference in coherent systems with Weibull models, without assuming independence or identical distributions.

Findings

Posterior distributions are proper even with non-informative priors.

The model performs well in simulations across different system complexities.

Application to real data demonstrates effectiveness with censored observations.

Abstract

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. It seems that the present paper is the first that presents the general case of component inferences in coherent systems. The failure time model considered here is the three-parameter Weibull distribution. Furthermore, neither independence nor identically distributed failure times are required restrictions. The proposed model is general in the sense that it can be used for any coherent system, from the simplest to the more complex structures. It can be considered for all kinds of censored data; including interval-censored data. An important property obtained for the Weibull model is the fact that the posterior distributions are proper, even for non-informative priors. Using several simulations, the excellent performance of the model is illustrated. As a real example, boys first use of marijuana is considered to show the efficiency of the solution even when censored data occurs.