Optimizing inspection and maintenance decisions in degrading systems with quality-loss

This study presents a novel optimization framework for condition-based maintenance using a discrete-time absorbing Markov chain to balance maintenance costs and system availability. The framework employs a multi-threshold policy, in which degradation thresholds dynamically determine non-periodic inspection intervals and maintenance actions. The degradation process follows a continuous-time Gamma process. Preventive maintenance is triggered when degradation exceeds a preventive threshold but remains below the failure limit, whereas corrective maintenance occurs at the failure limit. The optimization ensures cost efficiency while maintaining availability above a predefined target. Key performance metrics, including degradation-dependent inspection costs, maintenance cycle length, and quality loss, are analytically derived and evaluated. Importantly, the total cost per unit time explicitly integrates a degradation-dependent quality-loss component alongside inspection, maintenance, and downtime costs, highlighting quality loss as a key driver of decision-making trade-offs. The framework jointly optimizes the number of degradation phases, inspection intervals, and degradation limits to minimize the total cost per unit time subject to an availability constraint. The mixed-integer nonlinear programming problem is solved using a two-stage approach: a greedy search to select the number of degradation phases, followed by a constrained nonlinear program to refine the inspection intervals and thresholds. Numerical results demonstrate cost-efficient policies with high availability, providing practical insights for decision-makers. The work presents a robust decision-support tool for managing complex degrading systems.