Stochastic analysis of a two unit adaptive system subject to slow switch with random service

Abstract

This paper considers a two-unit repairable shared parallel system with single service facility available at random. Initially, both the units share the total load equally and when one unit fails it goes for repair. Simultaneously, the other surviving unit takes over the entire load until the repair is completed and the repaired unit is ready for operation after installation. The installation time is assumed to be non-negligible. Failure rate of a unit when it is operating with full load is assumed to be greater than that of a unit, when it is operating with half load. The single service facility employed both to install a repaired unit and to repair a failed unit is available at random according to a known distribution k(.). Assuming that a unit has to undergo different types of repairs due to different loads with which it fails, the following system characteristics, namely, 1. (1) expected available time of the system 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], are evaluated to carry out the cost-benefit analysis.