Abstract
This paper deals with the cost-benefit analysis of a single-server two-unit repairable system with a warm (partially energised) standby subject to inspection. Two inspection strategies are proposed, namely: (i) failure of the operating unit as well as the standby unit are detected by inspection only, but system failure is detected instantaneously without inspection; (ii) failure of the operating unit and the standby unit as well as system failure are detected by inspection only. It assumes that the failure times of the units are exponentially distributed with parameters λ and λ 1, 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. System characteristics, namely: 1. 1. point-wise availability of the system in (0, t]; 2. 2. s-expected up-time of the system in (0, t]; 3. 3. s-expected busy-period of the service facility in (0, t]; 4. 4. s-expected net gain per unit time in (0, t]; 5. 5. steady-state availability of the system, are obtained to carry out the cost-benefit analysis. Numerical results pertaining to two particular cases are presented.
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