Modeling of machine interference problem with unreliable repairman and standbys imperfect switchover

Highlights: • We study an M/G/1 machine interference problem with an unreliable repairman and imperfect switchover of standbys. • Using the method of supplementary variable, the stationary probability distribution is obtained. • Some performance measures and system reliability indices are developed. • We discuss the cost effectiveness maximization. • A cost model is constructed to find the optimal numbers of primary and standby substations. This investigation is concerned with an M/G/1 machine interference problem with imperfect switchover of standbys, in which an unreliable repairman maintains a group of machines. An unreliable repairman means that the repairman is typically subject to unpredictable breakdowns. The time between two consecutive breakdowns follows an exponential distribution, and recovery time of the unreliable repairman follows a general distribution. The lifetime of operating/standby machines and the repair time of failed machines are exponentially and generally distributed, respectively. Using the method of supplementary variable, the stationary probability distribution is obtained. We develop some performance measures and system reliability indices. Furthermore, the cost effectiveness maximization is also discussed. Finally, a cost model is proposed to find the optimal numbers of operating and standby substations, which minimize the average cost per unit time.