Analysis on Nonmonotone Control-Limit Condition-Based Maintenance Policies

This study delves into the challenge of optimizing condition-based maintenance (CBM) for $k$-out-of-$N$ systems characterized by economic dependencies, utilizing an average cost Markov decision process formalism for a detailed analysis of optimal policies. Traditionally, CBM optimization presumes a monotone control-limit policy where the degradation level of components exceeds predefined thresholds. Recent investigations have visually demonstrated that the optimal CBM policy exhibits a nonmonotone structure. Our analysis reveals that although the optimal bias functions exhibit partial monotonicity, this characteristic alone does not guarantee a monotone CBM policy. The emergence of nonmonotonicity is attributed to the dynamics of the transition matrix influenced by preventive maintenance activities. In addition, we show that the cost function is subadditive, indicating that the presence of setup costs significantly influences maintenance decisions, where this subadditivity also affects the formation of nonmonotone regions in the optimal policy. Our findings indicate that nonmonotone regions persist even in the absence of economic dependencies. Sensitivity analysis further reveals that higher cost parameters and reliability structure reduce the ratio of nonmonotone regions, enhancing system stability. This study emphasizes the complex interdependence between reliability structure and cost parameters in shaping optimal CBM policies.