On the expected net revenue of a one-server two-unit system with arbitrary installation time

Abstract

This paper considers a two-unit cold standby repairable system subject to slow switch under the assumption that the standby unit is replaced if the basic unit is ready for operation after repair and installation. The failure rates of the units are assumed to be constants while the installation times and the repair times of the units are non-negligible and are arbitrarily distributed. The system is characterized by the probability of its being in up or down state at a given instant. Integral equations are set up for these probabilities by identifying the system at suitable regeneration epochs. The cost-benefit analysis of the system is carried out by finding the following system's characteristics: 1. (1) expected up-times of the units during the period (0, t], 2. (2) expected repair times of the units during the period (0, t] and 3. (3) expected time spent by the units in the installation state during the period (0, t].