Bayes Estimation of Reliability for Special k-out-of-m:G Systems

Component lifetimes of a k-out-of-m: G system are s-independent and exponentially distributed. The Bayes-quadratic-loss estimator of reliability for the system is obtained using a conjugate (1-parameter case) or a noninformative (2-parameter case) prior when data are type-II censored. A simple approximation formula for the mean square error of the Bayes estimator is proposed. Based on the mean square-error criterion, the performance of the Bayes estimator under a noninformative prior is compared with that of the maximum likelihood and minimum variance s-unbiased estimators.