Optimizing alternate replacement strategy of k-out-of-n: F systems with common-mode degradation: An application to railway grid

Under the grid management framework for railway lines, each rail grid consists of several adjacent steel rails. The degradation processes of the steel rails within a grid are characterized by common-mode deterioration due to their similar spatial locations and accumulated gross tonnages. Additionally, in line with the railway repair and maintenance regulations, comprehensive replacements of rail grids are prohibited during the summer months, and similar restrictions apply in winter. To effectively minimize the operating and maintenance costs associated with a rail grid over a one-year period, this study develops a k-out-of-n: F system model that incorporates common-mode degradation. A dynamic and alternate replacement strategy is proposed, focusing on both system-level and component-level interventions. The degradation of each steel rail is modeled using a Gamma process, while the dependence structure of the system is characterized through a copula function. The maintenance model is structured as a Markov Decision Process (MDP). To address the MDP problem, approximate and analytical expressions for discretized state transition probabilities within the multiple-component system are derived. These expressions are determined using the copula function, and an algorithm is designed to construct the corresponding transition probability matrix. The monotonicity of value functions is also explored. A numerical example is provided to demonstrate the feasibility and effectiveness of the proposed model.