An optimal opportunistic maintenance policy for a two-unit series system with general repair using proportional hazards models

Abstract

This paper proposes an opportunistic maintenance policy for maintaining mechanical systems consisting of two series units with economic dependency. Condition monitoring and age information is available for unit 1 and unit 2, respectively. A gamma process describes the stochastic deterioration of unit 1, and condition monitoring data is utilized to estimate its hazard rate using the proportional hazards model (PHM). A matrix-based algorithm is employed to derive the conditional reliability of a two-unit series system with a continuous-state deterioration process. The policy proposes preventive actions on scheduled intervals, based on lifetime and PHM parameters, to enhance system reliability and mitigate unexpected downtimes. Corrective actions rectify the failed unit, while the other unit can be maintained opportunistically. The problem is formulated as a semi-Markov decision process (SMDP) with an objective of minimizing the long-run expected average cost over an infinite time horizon. This paper relaxes a common assumption that repair brings the units to the as-new condition, and provides solutions for the maintenance scheduling of two-unit series systems, where repair is also allowed.