A Markov repairable system involving an imperfect service station with multiple vacations

The main purpose of this paper is to study the reliability and availability of a system with M operating devices, m spares, and an imperfect service station that takes vacations. Specifically, once there are no failed devices in the system, the service station takes consecutive vacations until there is at least one failed device upon its return from vacation. The service station may break down and require repair at a repair facility. This paper derives the reliability, the mean time to system failure, the availability, and failure frequency of the K-out-of-M + m system. Numerical simulation of the impacts of system parameters as well as sensitivity analysis for the reliability, the mean time to system failure, the availability and failure frequency is performed.