Probabilistic Analysis of a Two-Unit System with a Warm Standby and a Single Repair Facility

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Abstract
This paper deals with the availability and the reliability of a two-unit system with a warm standby and subject to a single repair facility. It assumes the failure times of the units to be exponentially distributed with parameters λ and λ1, respectively. Initially, a unit is switched on and the other one is kept as a warm standby. The system breaks down if a unit fails while the other is still under repair. This paper characterizes the system by the probabilities of its being in the up or the down state, sets up integral equations for these probabilities by identifying suitable regenerative stochastic processes, and employs the Laplace-transform technique to solve these equations. It obtains the mean down-time of the system during (0, t) and the mean time to system failure explicitly.

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