ABSTRACT
This chapter applies the theory of aggregated stochastic processes to derive the formulas for the distribution of time to first failure, point-wise, and interval availabilities of the new proposed repairable system. A reliability analysis of a Markov repairable system has been a hot topic for some time and various models based on Markov processes have been developed. B. Liu et al. proposed a cold standby repairable system with working vacations and vacation interruption following a Markovian arrival process. The chapter discusses reliability indexes such as the distributions of the time to first failure, mean time to first failure, point-wise availabilities, steady availabilities and interval availabilities under two cases when τ is a constant and a random variable. It examines several reliability indexes of systems under the circumstances when τ is a constant or a random variable respectively.
