Condition-Based Selective Maintenance Optimization for Large-Scale Systems Consisting of Many Homogeneous Units

This study considers a maintenance optimization problem for a large-scale system comprising many homogeneous units. Each unit degrades by transitioning on predefined health states, where transition times follow general distributions from one state to another. We consider a selective maintenance scheme where one can repair or replace units under specific health states at each maintenance activity. The system, therefore, does not seem to have a regenerative nature because some units still remain in their degraded states after maintenance. This selective nature challenges the analysis and maintenance decision-making. We first formulate such a process as a fluid system to characterize the degradation pattern at the system level. Based on the fluid model, we devise a condition-based maintenance policy that triggers a repair action when the weighted sum of the fraction of units in specific health states hits a predetermined threshold. Our implementation finds that the fluid system shows periodic behavior as time goes by; the system becomes asymptotically regenerative. Hinging upon this observation, we develop an algorithm to find a threshold triggering a maintenance action that minimizes the long-run average cost. Numerical experiments show that the proposed fluid model accurately approximates the dynamics of system degradation, and the condition-based selective maintenance scheme is cost-effective against the alternative periodic maintenance strategy.