Reliability analysis of a <i>k</i>-out-of-<i>n</i>:<i>G</i> system with general repair times and replaceable repair equipment

Abstract

This paper studies a k-out-of-n:G repairable system with one replaceable repair equipment, where the lifetimes and repair times of components follow exponential distributions and arbitrary distributions, respectively. When one component breaks down, it is repaired by the repair equipment. Further, the repair equipment may fail during the repair period and then be replaced by a new one. The replacement time of the repair equipment is a generally distributed random variable. Employing the semi-Markov process theory and the Laplace (Laplace–Stieltjes) transform, the mean time to the first failure, the steady-state system availability, the rate of occurrence of failures of the system, the probability that the repair equipment is being replaced and the rate of occurrence of failures of the repair equipment are derived. Meanwhile, some numerical illustrations are reported to demonstrate how the various parameters of the model influence the behaviour of the system. Finally, a special case -out-of-n:G repairable system is discussed to validate the correctness of the theoretical results.