Semi Markov Approach for Asymptotic Performance Analysis of a Standby System with Server Failure

this paper the asymptotic performance of a cold standby system with two identical units is analyzed. When a unit fails it is inspected by a server to check the feasibility of repair or replacement. If repair is not feasible, unit is replaced by new. The server is subjected to failure while performing its job. The system model is developed using semi-Markov approach of Markov processes. The regenerative point technique is used to derive expressions for various measures of system performance. The random variables associated with the system (failure time, inspection time, repair time, treatment time) are assumed to follow arbitrary distribution with different probability density functions. A numerical study is also presented to demonstrate the practical importance of the research.