Availability and maintenance strategy under time-varying environments for redundant repairable systems with PH distributions

Systems commonly operate in time-varying environments which have essential impact on system performance, thus reliability modeling and maintenance strategy are faced with new challenges. In this study, a cold standby repairable system in a time-varying environment is investigated based on different operational levels and maintenance strategies, in which repairman's vacation and maintenance rules vary with environments. The evolution of dynamic environments is governed by a Markov process, and the successive vacation time is governed by Markovian arrival processes (MAPs). Using Phase-type (PH) distribution not only increases the flexibility of analytical properties because it can approximate to any probability distribution defined on a nonnegative real line, but also could effectively ensure the applicability of the model in engineering practice, specially all the lifetimes of components and maintenance time are subject to disparate PH distributions in diverse environments. By employing the matrix-analytic method, Kronecker operator theory and aggregated stochastic processes, some reliability indexes and the system average benefit are obtained respectively. Finally, an example of a redundant power supply is given to illustrate the validity and applicability of the proposed model.