Application of degradation growth model in the estimation of Bayesian system reliability

Abstract

In real life situations, for example, in case of concrete structures and mechanical devises, failure occurs due to accumulation of stress over time, and the consequent degradation causes the system to under-perform, thereby failure occurs completely, when the accumulated stress exceeds a critical threshold. The degradation path is known for some systems and in such cases useful information on product reliability can be obtained from these measurements. This work considers a degradation model having exponential degradation path with positive degradation rate, which follows Weibull distribution with known shape parameter β, and unknown scale parameter α. The Bayesian analysis is performed by considering noninformative (Quasi) and informative (Gamma) prior distributions for the scale parameter α. The Bayesian estimators of α and the system reliability are presented as well. The standard error for estimated α corresponding to both informative and noninformative priors are calculated using bootstrap method. It is observed that for larger bootstrap sample, the Bayes estimator of α, tends to have minimum standard error. It is also seen from the simulation study carried out by making use of Gibbs sampling technique that the Bayesian reliability of the system approaches the actual reliability for increasing sample size.