Conditional Hitting Time and Mean Residual life in Semi-Markov Models

Abstract

Abstract The mean residual life (MRL) in the repairable systems will have been introduced and a formula for its calculating presented based on the conditional distribution of the excess life for semi-Markov processes (SMPs). Moreover, the first hitting time to some specified state given the past history of the SMP has been presented besides calculating its expected value. By the best of our knowledge, it seems that there does not exist any specific research related to the issue of the MRL function in the area of repairable systems with semi-Markov structure. Nevertheless, there are a large amount of studies related to the various aspects of reliability systems, where almost all of them employ the MRL function and emphasis on the significant importance and applications of it. So, these studies and applications motivated us to examine the MRL function for repairable systems. As an application, a two unit cold standby system with a repairman has been considered as a semi-Markov model and the associated MRL has been studied in details.