A Structural Property of Optimal Policies for Multi-Component Maintenance Problems

In this paper, we focus on the opportunistic maintenance of an asset which is composed of multiple nonidentical life-limited components with both economic and structural dependence. Besides the random asset failure, each component also has independent failure with constant rate. Both finite and infinite horizons are considered. We first prove the optimality of the Generalized Strict Shortest-Remaining-Lifetime-First (GSSRLF) rule to efficiently reduce the size of the action space from O(2ⁿ) to O(II_i=1^m= n_i), where n is the number of components, m is the number of modules, and n_i is the number of components in module i . Then, we show that the GSSRLF rule is more general than the existing SRLF rule, and has close relationship with several other rules and properties known in literature. Finally, we discuss the limitations of the GSSRLF rule and use numerical results to show that even when the rule is not optimal, it helps to identify good policies.