Joint optimization of reallocation and replacement policies for k -out-of-2 n: F balanced systems subject to hierarchically stochastic dependence

In small-radius curved railway sections, outer rails in symmetric slots experience far more severe wear than their inner counterparts. Such asymmetric wear accelerates the performance degradation of the wheel-rail system and reduces the operational efficiency of rail transit systems. The wear of a single rail is the superposition of its inherent wear and two types of additional wear. One is induced by small curve radius and gross traffic tonnage, while the other originates from its location in the curve. Considering the unique balance mechanism and degradation behaviors of rails, this study proposes a k -out-of-2 n: F balanced system subject to hierarchical stochastic dependence. The degradation process of the system is modeled using a 2 n -variate Gamma subordinator constructed from 3 n + 1 univariate Gamma processes. The balance degree of the system is quantified by the state discrepancies between paired components in symmetric slots. To copy with the degradation heterogeneity among components, the distinctive balance mechanism of the system, and practical engineering requirements, a hybrid maintenance policy integrating rail reallocation and component-level replacement actions is developed. A multi-stage Markov decision process (MDP) model is formulated to derive the optimal maintenance policy for minimal total cost over a finite planning horizon. The expectation-maximization (EM) algorithm is adopted to calculate the maximum likelihood estimators of degradation parameters. Numerical examples and comparative analyses verify the feasibility of the proposed model and illustrate its superiority over alternative approaches.