A repairable system with imperfect coverage and reboot: Bayesian and asymptotic estimation

System characteristics of a two-unit repairable system are studied from a Bayesian viewpoint with different types of priors assumed for unknown parameters, in which the coverage factor for an operating unit failure is possibly considered. Time to failure and time to repair of the operating units are assumed to follow exponential distributions. In addition, the recovery time and reboot time of the failed units also follow exponential distributions. When time to failure, time to repair, recovery time and reboot time are 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.