Reliability estimators for the components of series and parallel systems: The Weibull model

TL;DR

This paper introduces a hierarchical Bayesian Weibull model for estimating component reliability in series and parallel systems, effectively handling censored data with a flexible prior structure.

Contribution

It develops a novel hierarchical Bayesian framework that incorporates gamma and uniform priors for Weibull parameters, enabling robust reliability estimation with censored data.

Findings

Effective estimation with censored data demonstrated

Hierarchical Bayesian approach improves reliability estimates

Simulation study validates model performance

Abstract

This paper presents a hierarchical Bayesian approach to the estimation of components' reliability (survival) using a Weibull model for each of them. The proposed method can be used to estimation with general survival censored data, because the estimation of a component's reliability in a series (parallel) system is equivalent to the estimation of its survival function with right- (left-) censored data. Besides the Weibull parametric model for reliability data, independent gamma distributions are considered at the first hierarchical level for the Weibull parameters and independent uniform distributions over the real line as priors for the parameters of the gammas. In order to evaluate the model, an example and a simulation study are discussed.