基于 phase⁃type 分布与动态规划的多状态系统视情维修优化

Condition⁃based maintenance (CBM) has become an important theory for enhancing system reliability and controlling maintenance costs by utilizing system state information for maintenance decision⁃making. This paper proposes a CBM optimization method based on phase⁃type(PH) distribution and dynamic programming for complex series⁃parallel multi⁃state systems commonly found in practical engineering (e. g., industrial production line sys⁃ tems) . Firstly, the degradation process of multi⁃state components is modeled as a continuous⁃time Markov chain using PH distributions, which enables flexible approximation of various lifetime distributions and enhances the model′s generalization capability. Based on this, a maintenance optimization model is then formulated with the objective of minimizing the total maintenance cost, subject to constraints on system reliability and cost budget. To solve the model accurately, a dynamic programming algorithm incorporating a sparse node strategy and a solution space reduction technique is proposed for the first time to obtain the global optimal maintenance strategy. Finally, a case study on a critical parts production line system for an aero⁃engine, along with numerical simulation experi⁃ ments, verifies the adaptability and effectiveness of the proposed method in maintenance optimization engineering.