Load-sharing and maintenance policy for two-unit systems under dependent bivariate degradation processes

Given that workload allocation can significantly impact the deterioration rate of units, decision-making regarding load-sharing and maintenance must consider the complex and dynamic interactions between unit deterioration and the allocated workload. This research focuses on condition-based maintenance for a system comprising two units with mutually dependent deterioration processes. A joint optimal load-sharing and maintenance policy with flexible load-sharing is proposed for two-unit deteriorating systems under a constant total workload. The underlying deterioration process of the system, which depends on the workload allocation, is modeled using a bivariate gamma degradation process. Based on the system's deterioration state, the decision - maker determines whether to continue operating the system for an additional period with a specific load allocation ratio or to initiate maintenance on any unit. The optimization problem is formulated as a Markov decision process that minimizes the total expected cost over an infinite horizon. The properties of the proposed optimal decision policies are investigated through simulation results, and the performance of the proposed policy is evaluated by comparing it to a policy with equal workload distribution. Additionally, a sensitivity analysis is conducted to illustrate the effects of economic and deterioration dependencies on load-sharing.