# Dynamic Preventive Maintenance Optimization of Subway Vehicle Traction System Considering Stages
## 2 Maintenance Strategy Ideas
### Single-Component Maintenance Strategy Description and Assumptions  
According to the current maintenance management method of subway vehicles, a component dynamic reliability model is established considering the dynamic decline of component reliability during service. Taking the key components in the traction system of subway vehicles as the research object, the \"non-new and non-old\" preventive maintenance is carried out. In order to improve system reliability and reduce vehicle downtime for maintenance, the reliability status of key components is monitored. The dynamic reliability of key components is used as a judgment index to determine the timing of preventive maintenance. Maintenance methods include preventive maintenance, preventive update maintenance, and non-preventive failure maintenance. The maintenance costs and losses caused by the three maintenance methods are considered. The goal is to minimize the total maintenance cost per unit time. Maintenance method, maintenance interval, and update timing are determined. When the reliability of the component is lower than its reliability threshold, corresponding maintenance methods need to be taken, as shown in Figure 1.  
The component operation reliability is monitored. The operation status of the component is obtained. Based on the monitored operation status, the following maintenance activities are formulated:  
1. When \(R(t)>R(t_{m})\), that is, \(R\big{(}t_{j1}\big{)}\), the operation state of the components is acceptable, and no maintenance measures are required. \(t_{m}\) is the time when the component is in preventive maintenance or preventive update maintenance. \(t_{j1}\) is the moment when the component is in operation. 2. When uncertainty, that is, \(R\big{(}t_{j2}\big{)}\), a component fails non-preventatively and failure repair is performed. \(t_{j2}\) is the moment when the component is in non-preventive failure maintenance. 3. When \(R(t)\leq R(t_{m})\), the reliability of the component is lower than the preventive maintenance threshold, and preventive maintenance must be carried out. The reliability of the repaired component is improved but not restored to a new state. If it is not economical to preventively maintain a component, it must be updated. Then, the component will be in a new state after the update. In order to ensure the generality of the preventive maintenance model of subway vehicles, the following basic assumptions are made first. Then, a single-component preventive maintenance strategy model is established. 1. The failure rate of the component follows an exponential distribution or a Weibull distribution. 2. The components operate from an as-new condition and continue to operate during the monitoring period. 3. Non-preventive maintenance can restore component performance in a timely manner. However, the failure rate remains the same before and after maintenance, and can be repaired in time. 4. A component is subject to preventive maintenance without regard to its negative impact on the reliability of the component. The component reliability is improved and restored to a \"not new, not old\" condition. 5. The components are in an as-new condition after preventive update maintenance. Figure 1: Corresponding relationship between reliability and running time of component. For different maintenance methods, the maintenance costs and losses are different. However, the downtime cost of preventive maintenance and non-preventive failure maintenance per unit time is the same for different components. The description and assumptions of the maintenance strategy are referenced. \(T_{i}\) represents the interval between the \(i-1\)-th and the \(i\)-th maintenance of the component. When the component undergoes the \(N+1\)-th preventive maintenance, the failure rate is increasing as the previous \(N\) preventive maintenance is carried out, and failure rates have increased to an unacceptable level. It is not economical to continue preventive maintenance. Therefore, the \(N+1\)-th preventive maintenance adopts preventive update maintenance.