Probabilistic Analysis of a Multicomponent Series-Parallel System under Preemptive Repeat Repair Discipline

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Abstract
This paper considers a system consisting of two subsystems connected in series with a single repair facility. One subsystem consists of M identical units connected in parallel, while the other consists of several different units connected in series. The units' failure times are exponentially distributed, whereas repair times are distributed quite generally. Initially, the system is in any one of the operative states. The system breaks down if all the units in the parallel group are simultaneously in failed states or if any failure occurs in the series group. The availability and reliability function of the system are obtained simultaneously. We use a suitable transformation to deduce the reliability from the availability function. Explicit expressions for the steady-state availability of the system and the mean time to system failure are obtained. The mean time to system failure and the mean down time as new measures in equilibrium are defined and then obtained explicitly.

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