Multilevel preventive replacement for a system subject to internal deterioration, external shocks, and dynamic missions

Mission-oriented systems have received intensive attention for extensive applications. Existing maintenance policies focus mainly on unvarying missions, which is inconsistent with many mission-oriented systems. This paper develops a condition-based replacement model for a mission-oriented system subject to internal deterioration, external shocks, and a sequence of random missions. The deterioration level is revealed by condition monitoring performed at the end of each mission. If it exceeds a critical level, both the system and the previous mission fail, resulting in a corrective replacement cost and a penalty for the failed mission. Otherwise, the decision-maker can decide whether to replace the system preventively. This paper proposes a multilevel preventive replacement policy that involves a set of replacement thresholds corresponding to all mission types. The objective is to determine the optimal set of thresholds to minimize the long-run expected average cost per unit time. The optimization problem is formulated in the Markov decision process framework based on a discretization method. An efficient optimization algorithm combining stochastic dynamic programming and Nelder-Mead search is developed to find the optimal policy. Results from a numerical study confirm the effectiveness of the proposed approach.