Optimal Selective Maintenance Strategy for Multi-State Systems Under Imperfect Maintenance

TLDR

Many industrial systems perform missions with limited downtime, and selective maintenance is commonly used to ensure mission success under resource constraints, yet most existing optimization studies address only binary‑state systems while real‑world systems often involve multiple deterioration states. This study develops a selective maintenance policy for multi‑state systems composed of binary‑state elements. By incorporating imperfect maintenance quality through a Kijima‑based cost–age reduction relationship, formulating mission success probabilities with a universal generating function, and solving the resulting optimization with a genetic algorithm, the authors provide a tractable solution framework. A coal‑transportation power‑station case study shows the method’s effectiveness, and comparison with perfect‑maintenance strategies confirms that accounting for imperfect maintenance quality yields superior outcomes.

Abstract

Many systems are required to perform a series of missions with finite breaks between any two consecutive missions. In such a case, one of the most widely used maintenance policies is a selective maintenance in which a subset of feasible maintenance actions is chosen to be performed with the aim at achieving the subsequent mission success under limited maintenance resources. Traditional selective maintenance optimization reported in the literature only focuses on binary state systems. Most systems in industrial applications, however, have more than two states in the deterioration process. In this work, a selective maintenance policy for multi-state systems (MSS) consisting of binary state elements is investigated. Taking the imperfect maintenance quality into consideration, the Kijima model is reviewed, and a cost-maintenance quality relationship which considers the age reduction factor as a function in terms of maintenance cost is established. Moreover, with the assistance of the universal generating function (UGF) method, the probability of the repaired MSS successfully completing the subsequent mission is formulated. In place of enumerative methods, a genetic algorithm (GA) is employed to solve the complicated optimization problem where both multi-state systems, and imperfect maintenance models are taken into account. The effectiveness of the proposed method is demonstrated via a case study of a power station coal transportation system. Finally, a comparative analysis between the strategies with and without considering imperfect maintenance is conducted, and it is concluded that incorporating imperfect maintenance quality into selective maintenance achieves better outcomes.