Robust selective maintenance strategy under imperfect observations: A multi-objective perspective

Selective maintenance, as a pervasive maintenance policy in both military and industrial environments, aims to achieve the maximum success of subsequent missions under limited maintenance resources by choosing an optimal subset of feasible maintenance actions. The existing works on selective maintenance optimization all assume that the condition of components in a system can be perfectly observed after the system completes the last mission. However, such a premise may not always be true in reality due to the limited accuracy/precision of sensors or inspection instruments. To fill this gap, a new robust selective maintenance model is proposed in this work to consider uncertainties that originate from imperfect observations. The uncertainties associated with imperfect observations are incorporated into the states and effective ages of components via Bayes rule. The Kijima type II model, as a specific imperfect maintenance model, is used to characterize the imperfect maintenance efficiency of each selected maintenance action. The expectation and variance of the probability of a repairable system successfully completing the subsequent mission are derived to quantify the uncertainty that is propagated from imperfect observations. To guarantee the robustness of a selective maintenance strategy under uncertainties, a multi-objective selective maintenance model is constructed with the aims of maximizing the expectation of the probability that a system successfully completes the subsequent mission and to simultaneously minimizing the variance in this probability. The Pareto-optimality approach is utilized to offer a set of non-dominated solutions. Two illustrative examples are presented to demonstrate the advantages of the proposed method.