Probabilistic analysis of a series–parallel repairable system with three units and vacation

This paper studies the steady-state availability and the mean up-time of a series–parallel repairable system consisting of one master control unit, two slave units and a single repairman who operates single vacation. Under the assumption that each unit has a constant failure rate and arbitrary repair time distribution, by using the supplementary variable method and the vector Markov process theory, we obtain the explicit expressions for the steady-state probabilities of the system, the steady-state availability and the mean up-time. A special case without vacation is given. Numerical results are provided to investigate the effects of various system parameters on the steady-state availability and the mean up-time.