Availability analysis and cost optimization of a repairable system with a mix of active and warm-standby components in a shock environment

The mixed redundancy strategy is a recently introduced powerful redundancy technique for improving system reliability. So far, the performance of the mixed redundancy strategy is just analyzed in systems with cold standby components. In the present study, for the first time, a 1-out-of-n:G repairable system under the mixed redundancy strategy with warm-standby components is investigated. Furthermore, it is assumed that the system and all its components are under environmental shocks, where components may deteriorate by internal wear or the arrival of external shocks. The active and standby components are exposed to the external shocks imposed by two different resources, and their arrivals are governed by Markovian arrival processes. Therefore, the system's behavior is modeled by a Markov chain approach, and some performance measures are derived according to matrix-analytic procedure. Besides, an age-dependent maintenance strategy is applied to the proposed system, and a cost optimization problem is formulated to obtain the optimal system replacement time. Finally, to justify the presented method, two numerical examples are studied. The first one aims to illustrate the performance of the system in both transient and stationary regimes. The second example tries to deal with availability and cost objective functions while finding the optimum replacement time.