Analysis of a two-unit standby system with fixed allowed down time and truncated exponential lifetime distributions

This paper deals with the profit analysis of a single-server two-unit (priority and ordinary) cold standby system model. The priority (p) unit has three modes—normal (N), partial failure (P) and total failure (F), whereas the ordinary (o) unit has only two modes—normal (N) and total failure (F). The system remains down for some fixed time T_d if during the repair of the o-unit, the p-unit fails totally. The distributions of time to failure for the p- and o-units from the N-mode are taken as truncated exponentials with different parameters, while the other time distributions are negative exponentials. By identifying the system at suitable regenerative epochs, the profit functions under two different policies are obtained.