On sequence planning for selective maintenance of multi-state systems under stochastic maintenance durations

In many industrial and military environments, systems are required to execute a sequence of missions with a finite break between two adjacent missions. Due to the limited maintenance resources, such as budget, time, and manpower, etc., it is oftentimes impossible to perform all the desirable maintenance actions in the break. In such circumstance, selective maintenance is able to identify a subset of feasible maintenance actions to be conducted, so as to guarantee the success of the next mission. In this paper, a new selective maintenance model for multi-state systems is developed to maximize the probability of a system successfully completing the next mission, while taking account of the stochasticity of the durations of breaks and maintenance actions. Due to the presence of these duration uncertainties, it necessitates (1) choosing a subset of maintenance actions from all the optional maintenance actions, and (2) planning a sequence of selected maintenance actions to be performed. The saddlepoint approximation is utilized to facilitate the computation of the involved multi-dimensional integration in evaluating the probability of a system successfully completing the next mission. The resulting constrained combinational optimization problem is resolved by a tailored ant colony optimization algorithm. A numerical example of a three-unit multi-state system, together with an illustrative example of a multi-state coal transportation system, is presented to examine the effectiveness of the proposed method.