Bayesian shrinkage estimation of reliability in parallel system with exponential failure of the components

The paper presents a Bayesian shrinkage method of estimating the reliability of a parallel system with identical exponential distribution of failure times. Data is available from type II censored samples. Thompson (J. Am. Statist. Ass.63, 113–123, 1968) proposed the ordinary shrunken estimator ?θ + (1-?)θ₀, with ? a constant (0 ? ? ? 1) and θ₀ the prior or guess value of θ, which is more efficient than the unbiased estimator θ if θ is close to θ₀ and is less efficient otherwise. Here we postulate a prior distribution of θ around θ₀ and use an ordinary Bayes estimator of θ instead of θ₀ in the ordinary shrunken estimator. The Bayesian shrinkage estimator of parallel system reliability has thus been obtained and Monte Carlo study of its efficiency with respect to unbiased and maximum likelihood estimators (mles) was conducted. It was found that the proposed estimator is better.