Optimal condition-based maintenance decisions for group-replacement multi-component repairable system

Multi-component replacement repairable systems refer to systems wherein all critical components are replaced in batches after a given production cycle, while defective parts are taken offline for maintenance before being reused as the system continues to operate. This paper focuses on multi-component replacement repairable systems composed of multiple identical components, defining a grouped replacement and offline condition-based maintenance strategy. The concept of maintenance degree is introduced to indicate the extent of maintenance on a component, and a model is constructed where maintenance effects, costs, and durations are determined by this degree of maintenance. By analyzing the state transition characteristics of the system operating under alternating conditions of operational and replacement components, a steady-state probability model of system degradation is derived. Considering factors such as maintenance time, cost, and effectiveness, an average cost rate model within a finite time frame is established to determine the optimal system replacement period, preventive maintenance thresholds, and degree of maintenance. The correctness and effectiveness of the strategy and model are verified using a seven-roll continuous hot-rolling system as a case study, along with an analysis of parameter sensitivity.