Formula omitted]-Expected number of repairs from online, standby and frequency of failures of a 1-server 2-unit warm standby system

Abstract

A 1-server 2-unit partially energized standby system is studied under the assumption that the repair times of online unit and standby unit are arbitrarily distributed while the failure time distribution of online unit is exponential and standby unit is arbitrary. The system is observed at suitable regenerative epochs to obtain the following system characteristics: 1. (i) s -expected number of repairs in (O,t] 2. (ii) s -expected number of repairs in (O,t] from online and standby 3. (iii) s -expected frequency of failures in (O,t]. Results pertaining to the case when all the distributions are exponential have been obtained. Also, the expressions in terms of Laplace transforms are given when both the repair time distributions are two-stage Erlangian and failure time of the standby is exponential.