Bayesian reliability estimation of a 1-out-of-k load-sharing system model

Abstract

The study deals with the reliability analysis of a 1-out-of-k load-sharing system model under the assumption that each component’s failure time follows generalized exponential distribution. With the assumption of load-sharing inclination among the system’s components, the system reliability and hazard rate functions have been derived. In classical set up, we derive maximum likelihood estimates of the load-sharing parameters with their standard errors. Classical confidence intervals and two bootstrap confidence intervals for the parameters, system reliability and hazard rate functions have also been proposed. For Bayesian estimation, we adopt sampling-based posterior inference procedure based on Markov Chain Monte Carlo techniques such as Gibbs and Metropolis–Hastings sampling algorithms. We assume both non-informative and informative priors representing the variations in the model parameters. A simulation study is carried out for highlighting the theoretical developments.