Maintenance optimization of a two-component system with mixed observability

This paper studies maintenance optimization for a two-component system under mixed observability. Component~$U_1$ is fully monitored, whereas component~$U_2$ is only partially observable due to sensing limitations. The system exhibits unidirectional positive degradation dependence, in which the health state of component~$U_1$ influences the degradation process of component~$U_2$, but not vice versa. We propose a novel framework for modeling and optimizing maintenance decisions for such systems using a partially observable Markov decision process (POMDP). Under mild conditions, we analytically establish structural properties of the optimal maintenance policy. Baum-Welch algorithm with multiple sample paths is developed to estimate the unknown system parameters in the context of a covariate-dependent Hidden Markov Model. %from observational data with multiple trajectories. Numerical experiments demonstrate the effectiveness of the proposed parameter estimation and the maintenance policy. Across 64 instances, we show that it consistently outperforms classical threshold-based policies. Specifically, when the degradation of component $U_1$ is faster, it achieves maximal cost reductions of up to approximately $6\%$