Finite-Horizon Joint Optimization of Maintenance and Spare Parts Ordering for a Two-Unit System with Dependent Degradation

This paper investigates the finite-horizon joint optimization of maintenance and spare parts ordering for a two-unit series system with dependent degradation. A bivariate Gamma process models component degradation, and the joint probability distribution is derived and validated through simulation. A Markov decision process is established and a probability computation method based on the bivariate distribution is proposed. We design a backward dynamic programming algorithm with a grid search that can obtain the optimal inspection interval and joint policy. A case study on a water supply pipe system is conducted to verify the effectiveness of the proposed approach. The optimal joint policy reduces the cost by an average of 24.41% compared with (s, S) inventory policy across performance evaluation experiments under different parameter combinations.