Structural Properties of Optimal Maintenance Policies for k -out-of- n Systems with Interdependence Between Internal Deterioration and External Shocks

Many modern engineering systems, such as offshore wind turbines, rely on k -out-of- n configurations to ensure reliability. These systems are exposed to both internal deterioration and external shocks, which can significantly impact operational efficiency and maintenance costs, necessitating optimal maintenance policies. This study investigates an optimal condition-based maintenance policy for a k -out-of- n system, where each unit deteriorates independently following a gamma process and is subject to random external shocks that cause sudden jumps in deterioration. This study considers (1) stochastic dependencies among units, where shock-induced cumulative deterioration in one unit affects others, and (2) interdependencies between external shocks and internal deterioration, where internal deterioration influences external factors and vice versa. Using a Markov decision process framework, we derive an optimal maintenance policy that minimizes expected maintenance costs while incorporating these interdependencies. Under reasonable assumptions, we establish key structural properties of the optimal policy, enabling its efficient identification. A case study on offshore wind turbines demonstrates the effectiveness of the proposed approach, achieving up to a 9.9% reduction in maintenance costs compared to alternative policies. This cost reduction is achieved by optimizing the timing of preventive maintenance while incorporating the two aforementioned types of dependence into the decision-making process. Sensitivity analyses further explore the effects of cost parameters, deterioration rates, and shock characteristics, offering valuable insights into designing maintenance strategies for systems influenced by shocks and interdependent deterioration.