A deteriorating repairable system with stochastic lead time and replaceable repair facility

In this paper, a deteriorating repairable system with stochastic lead time and replaceable repair facility is studied. We assume that the spare system for replacement is available only by an order and the lead time for delivering the spare follows exponential distribution. Moreover, we also suppose that the repair facility may be subject to failure during the repair period. Under these assumptions, by using the geometric process and the supplementary variable technique, some important reliability indices such as the system availability, rate of occurrence of failure (ROCOF) and the probability that the system is waiting for replacement are derived. An ordering policy N − 1 and a replacement policy N based on the number of failures of the system are also considered. Furthermore, employing several Lemmas, the explicit expression of the average cost rate is derived. Meanwhile, the optimum value N∗ for minimizing the average cost rate could be determined numerically.

► We carry out an analysis of a repairable system with stochastic lead time and replaceable repair facility.
► We modify the previous reliability models and firstly introduce a stochastic lead time for procurement of the spare system.
► The ordering policy N − 1 is firstly proposed in this paper.
► The optimum value N∗ that minimize the long-run average cost rate for the system is determined numerically.