# Joint Maintenance Strategy Optimization for Railway
)1 State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China; [EMAIL_ADDRESS] (Q.G. )1 State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China; [EMAIL_ADDRESS] (Q.G. )1 State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China; [EMAIL_ADDRESS] (Q.G. )1 State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China; [EMAIL_ADDRESS] (Q.G. )1 State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China; 20114072@bitu. accelerates the damage of vehicle components, causes rail damage and brings losses to railway operations. Reprofiling is the primary method of wheelset maintenance, which recovers the shape of the wheelset. For every 1 mm increase in wheel flange thickness, the wheel diameter is reduced by about 4.2 mm [10]. Reasonable inspection intervals and reprofiling strategies of the wheel can avoid excess maintenance [11]. The cost of wheelset maintenance comprises a large percent of the maintenance budget for all railway operating companies [12]. Improving wheelset maintenance strategies can not only improve the safety level of rail transit, but it can also reduce maintenance costs. Research on wheelset maintenance strategies has been paid more and more attention in recent years. Some research focuses on wear prediction models and theories to forecast and assist maintenance decision making [13,14]. [PERSON] et al. [15] presented an early-stage data-based maintenance strategy to optimize maintenance intervals. Wheelset reprofiling strategies are developed based on wear analysis [16,17]. Data-driven analysis methods exploit information in historical data and are easy to implement. However, data-driven approaches are more focused on making the model fit the data, and the deterioration mechanism is rarely considered in these papers. Wheelset maintenance strategies are investigated by analyzing wheelset reliability [18]. [PERSON] et al. [19] proposed a maintenance model that considers wheelset aging and degradation for optimal inspection times. [PERSON] et al. [20] used classical and Bayesian semi-parametric degradation approaches to establish a hazard regression model to optimize wheel maintenance intervals. Reliability modeling is the foundation of maintenance optimization. Nevertheless, discussion of reprofiling strategies increases the difficulty of the reliability analysis of the wheelset, and thus, little attention is paid to reprofiling policies for wheelsets in this respect. Additionally, maintenance measures are developed by researching wheelset status evaluations. A data-driven evaluation model and an experience-based evaluation method for wheelsets support the maintenance decision [21,22]. The method can consider the wheelset status comprehensively. However, the evaluation process, such as selecting key indicators, is susceptible to subjective effects. To the best of our knowledge, only a small portion of the literature considers optimizing maintenance intervals and reprofiling strategies at the same time. In addition, revealing degradation mechanisms and understanding the wear law are important aspects of maintenance optimization research. According to a large number of studies on failure mechanisms, the essence of equipment performance degradation is caused by external shocks. To characterize the changes in performance through external shocks, [PERSON] et al. [23] proposed a shock model that is more physical and intuitive. Thus far, equipment reliability and maintenance strategy optimization have been studied based on the cumulative shock model [24, 25, 26, 27, 28, 29]. Equipment is subject to the competing failure of internal-based deterioration and external-based shocks to optimize preventive maintenance thresholds and periodic inspection intervals [30, 31, 32, 33]. The shock model can solve the problem of maintenance optimization very well.