Bayesian Analysis for a Redundant Repairable System with Imperfect Coverage

System characteristics of a redundant repairable system with two primary units and one standby are studied from a Bayesian viewpoint with different types of priors assumed for unknown parameters, in which the coverage factor is the same for an operating unit failure as that for a standby unit failure. Times to failure and times to repair of the operating and standby units are assumed to follow exponential distributions. When times to failure and times to repair with uncertain parameters, a Bayesian approach is adopted to evaluate system characteristics. Monte Carlo simulation is used to derive the posterior distribution for the mean time to system failure and the steady-state availability. Some numerical experiments are performed to illustrate the results derived in this paper.