# Dynamic Preventive Maintenance Optimization of Subway Vehicle Traction System Considering Stages
## 5 Example
### The Group Preventive Maintenance Model Validation  
The feasibility of the multi-component group preventive maintenance model (18) is verified. The four key components of pantograph, contactor, controller of main converter, and IGBT of metro traction system are analyzed. According to the data in Table 5, \(\lambda\) is a constant. It can be seen from Formula (1) that the failure rates of the four components obey the exponential distribution. That is to say, they are in the random failure stage. The running time of the components is 10 years, namely, \(D=3650\) days. Since the failure rate of the four components obeys an exponential distribution, only considering the service age decreasing factor after each preventive maintenance, it can be assumed that \(\alpha=1.1\). The parameters of the four components are shown in Table 5. \begin{table}
\begin{tabular}{c c} \hline \hline
**Maintenance Model** & **Maintenance Cost/CNY** \\ \hline Model of this paper & \(747\times 10^{4}\) \\ Current model & \(1218\times 10^{4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The total cost comparison results of the power supply module maintenance models. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Maintenance Model**} & **Optimum Preventive Maintenance** & \begin{tabular}{c} **Minimum Preventive Maintenance** \\ **Reliability Threshold** \\ \end{tabular} & \
\begin{tabular}{c} **Maintenance** \\ **Interval/d** \\ \end{tabular} &
\begin{tabular}{c} **Maintenance Model** \\ **/(CNY/d)** \\ \end{tabular} \\ \hline Model of this paper & 5 & 0.80 & 399-354-313-276-243 & 15.11 \\ Current model & 6 & 0.65 & 365-365-365-365-365 & 17.82 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison results of maintenance models for the power supply module. A calculation method for a single-component preventive maintenance strategy is adopted. Based on the parameters in Table 5, the preventive maintenance was performed for each component individually. The total maintenance cost during ten years of operation is 567,673 yuan. The parameters of Table 5 were substituted into the group preventive maintenance model (18). According to the model solving process in Figure 6, MATLAB is used to program the solution. The results are shown in Table 6.  
Table 6 only lists the situations where opportunistic maintenance occurs with the change of opportunistic maintenance threshold. That is, the total maintenance costs have changed. When \(\Delta t=69\), the four components group preventive maintenance mode changes again; but the controller was increased from 13 repairs in a decade to 14 at this time. There is excess maintenance, and the total maintenance costs increased. So, stop the cumulative value of \(\Delta t\). It can be seen from Table 6 that the appropriate \(\Delta t\) value has a crucial economic value impact on the total cost of group preventive maintenance. When \(\Delta t=65\), the total group preventive maintenance cost for the four components is the lowest. Therefore, the optimization result of opportunity maintenance threshold is \(\Delta t=65\). The individual preventive maintenance strategy and the group preventive maintenance strategy for the four components are shown in Figures 8 and 9, respectively. As can be seen from Figures 8 and 9, the maintenance frequency of implementing the group preventive maintenance strategy is relatively small. If preventive maintenance is performed on the four components individually, 38 repairs are required in ten years. Implementing a group preventive maintenance strategy, however, only required 20 repairs, a reduction of nearly 50%. It can be seen from Table 6 that in ten years, the total cost of implementing preventive maintenance for the four components individually is 567,673 yuan, and the total cost of implementing a group preventive maintenance strategy is 522,462 yuan, which can save 7.96%. In fact, the average annual maintenance cost for the traction system of a train is about 120,000 yuan (including the preventive update cost of components).