A standby repairable system with rest of server between repairs

A cold standby repairable system of two identical units has been analyzed stochastically in detail by considering the idea of rest of the server between repairs. The unit has two modes - normal and complete failure. There is a single server who is allowed to take rest before starting repair of the unit which was waiting for the repair. The random variables associated with repair and rest time of the server follow arbitrary distribution with different probability density functions while the failure rate of the unit is considered as constant. The semi-Markov process and regenerative point technique are used to derive the expressions for mean time to system failure (MTSF), availability, busy period of the server due to repair, expected number of repairs and profit function. The profit analysis of the system model has been carried out for particular values of the parameters. The profit of the system model has also been observed for change in the revenue per unit time, change in the cost for which server is busy due to repair and change in the cost per repair per unit time.