Bayesian assessing for a repairable system with standby imperfect switching and reboot delay

System performance measures of a repairable system are studied from a Bayesian viewpoint with different types of priors assumed for unknown parameters, in which the system consists of two active components and one warm standby. There is a failure probability q that switches from standby state to active state. Time-to-failure of components is assumed to be an exponential distribution. The reboot time and repair time are also exponential distributions. When time-to-failure, time-to-repair and reboot time are with uncertain parameters, a Bayesian assessing is adopted to evaluate system performance measures. Monte Carlo simulation is used to derive the posterior distribution for the steady-state availability and the mean time-to-system failure. Some numerical experiments are performed to illustrate the results derived in this article