# Dynamic Preventive Maintenance Optimization of Subway Vehicle Traction System Considering Stages
## 5 Example  
### The Single Component Preventive Maintenance Model Validation  
In order to verify the feasibility of the model (12), the power module in the traction inverter system is taken as the research object for analysis. According to the historical failure data of the power module and the experience of maintenance personnel, the parameter settings are shown in Table 1. It can be seen from Formula (2) that the failure rate of the power module obeys a two-parameter Weibull distribution, that is, \(\lambda(t)=\frac{\delta}{\eta}\left(\frac{t}{\eta}\right)^{\delta-1}\), \((\delta,\ \eta>0)\). The service age decreasing factor \(\alpha_{i}=0.1\) and the failure rate increasing factor \(\beta_{i}=1.1\) of the power module are assumed. Figure 6: Model solving process. Because \(\delta>1\), it means that the power module has entered the degradation stage. The parameters in Table 1 are substituted into Formulas (1)-(5). MATLAB is used to solve by programming. The interval between each preventive maintenance of the power module can be obtained. Then, each preventive maintenance interval is substituted into Formula (11). The maintenance cost per unit time can be obtained by programming. The results are summarized in Table 2. The change curves of the maintenance interval and maintenance cost rate of preventive maintenance are shown in Figure 7.  
It can be seen from Table 1 that when \(N=4\), the maintenance cost rate is the lowest, which is 15.11 yuan/day. From the moment the power module enters into degradation, preventive maintenance is required on days 399, 753, 1066, and 1342, respectively; and preventive update maintenance is performed on day 1585, or about 4.3 years. It can be seen from Figure 7 that the maintenance interval decreases with each preventive maintenance. It is consistent with the maintenance of the \"non-new and non-old\" model. The power module is updated maintenance by the subway operating company when it is overhauled. That is, the power module is used for 6 years after entering the degradation stage. Annual maintenance is implemented. The results of comparing the two maintenance models are shown in Table 3. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Parameter** & \(\eta\) & \(\delta\) & \(C_{p}\)**/CNY** & \(C_{lp}\)**/CNY** & \(C_{f}\)**/CNY** & \(C_{f}\)**/CNY** & \(C_{r}\)**/CNY** & \(T_{p}\)**/d** & \(T_{p}\)**/d** & \(R_{min}\) \\ \hline Value & 6.896 & 496 & 350 & 2000 & 230 & 10,000 & 2500 & 1 & 0.5 & 1.2 & 0.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter setting table for the power supply module. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Maintenance** & **Maintenance** & **Maintenance** & **Maintenance** & **Maintenance** & **Maintenance** \\
**Times** & **Interval/d** & **/(CNY/d)** & **Times** & **Interval/d** & **Cost Rate** \\ \hline
1 & 399 & 17.77 & 6 & 214 & 16.77 \\
2 & 354 & 15.55 & 7 & 188 & 17.50 \\
3 & 313 & 15.32 & 8 & 164 & 18.31 \\
4 & 276 & 15.11 & 9 & 144 & 19.16 \\
5 & 243 & 16.12 & 10 & 125 & 20.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Solution result of maintenance model for the power supply module. Figure 7: Curve of preventive maintenance interval time and maintenance cost rate for the power supply module. It can be seen from Table 3 that after the power module enters the degradation stage, the optimal preventive maintenance times of the model in this paper are 5 times; and preventive update maintenance is performed with the 5 th preventive maintenance. However, the minimum preventive maintenance reliability threshold for the current regular maintenance method is 0.65. Due to the low reliability, the number of non-preventive failures for the power module is increased. Ultimately, the maintenance cost rate is increased. It can be seen that the preventive maintenance model in this paper can not only ensure the reliability of components but also save maintenance costs.