Cost—benefit analysis of a one-server two-unit cold standby system subject to inspection
Abstract This paper deals with the cost—benefit analysis of a single-server two-unit cold standby redundant repairable system subject to inspection. An inspection policy model is considered in which the failure of a unit is detected by inspection only but system failure is detected instantaneously without inspection. The failure time of a unit is assumed to be exponentially distributed with parameter λ. Initially, a unit is switched on and the other one is kept as cold standby. The system breaks down if a unit fails while the other is still under repair. In this paper, the system is characterised by the probabilities of its being in the up or the down state. Integral equations are set up for these probabilities by identifying suitable regenerative epochs. Laplace transform technique is employed to solve these equations. System characteristics, namely: 1. pointwise availability of the system during (0, t 2. s -expected up-time of the system in (0, t 3. s -expected busy-period of the service facility in (0, t 4. steady-state availability of the system; are obtained to carry out the cost—benefit analysis. Numerical results pertaining to three particular cases are also presented.