Balancing downtime and maintenance costs for multi-component systems with economic and structural dependencies

We propose a comprehensive optimization framework for the preventive maintenance of multi-component systems with economic and structural dependencies. In this framework, the objective is to minimize the expected discounted total cost, including both downtime and maintenance costs, subject to system reliability requirements. Methodologically, our main contribution is the development of a unified modeling approach that integrates a binary decision diagram (BDD)-based representation of system reliability with a Markov Decision Process (MDP) formulation to guide sequential maintenance decisions. The BDD is an analytical expression of the system reliability as a function of component reliabilities, capturing the structural failure logic of general coherent systems, including series, parallel, series–parallel, and k-out-of-N configurations. This reliability representation is embedded in the MDP framework to evaluate the expected system downtime costs of different maintenance policies. Structural dependencies are implied by the system’s failure logic and the feasibility of maintenance actions, while economic dependencies arise from cost interactions among maintenance actions. In our model, it is possible to determine optimal maintenance policies under both types of dependencies. Numerical examples illustrate how the minimization of maintenance and downtime costs affects optimal maintenance decisions, including the optimal grouping of maintenance actions, as well as trade-offs between downtime and maintenance costs for different system designs and their cost parameters.