## 4 Case Verification and Result Analysis  
### Case Verification  
As shown in the figure, the equipment system consists of seven subsystems in series, each component in the system can be regarded as a multistate component with independent failure condition, and its mission capability is determined by the mission reliability of each subsystem. Table 1 lists the relevant parameters of various components in the system, including the shape parameter \(\beta\) of the Weibull life distribution, scale parameter \(\eta\), virtual age improvement factor m, maintenance cost corresponding to replacement and maintenance (unit: 10\({}^{3}\) yuan) and maintenance time (unit: min). The duration of the next mission is set to \(\tau=12\) min, and the maximum maintenance level is set to 15. Assume that the fleet consists of four vehicles of the same model. Figure 4: Selective maintenance planning algorithm flow of the two-stage equipment group. Figure 5: The vehicle system reliability block diagram. In order to make a selective maintenance decision on the fleet, the maintenance decision model is used to describe the problem, and the multiobjective sparrow search algorithm is used to solve the problem. The sparrow population size is set to 400, the maximum number of iterations is set to 1000 and the maintenance cost is capped at 35,000 yuan. After maintenance, the lower limit of the mission satisfied capability of the fleet is 0.7, and the upper limit of the storage of external files of the algorithm is 60. Some specific parameter settings are as follows: The safety threshold of the producers is set to 0.9. The mission duration is 12. The size of the sparrow population is 400. The maximum iteration of MSSA is 1000. The annealing rate is 0.99. The initial temperature and final temperature of SA are 1000 and 1, respectively. In this section, multiple tests are conducted on the equipment system under different initial health conditions, and the nondominated solution set is shown in Figure 6. Then, the optimal maintenance schedule and maintenance time corresponding to these strategies are obtained by SA algorithm. On this basis, the target space is divided into several parts according to the maintenance cost index, and the maintenance plan is determined according to the shortest maintenance time in each part. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**S** & \(N_{i}\) & \(\beta\) & \(\eta\) & \(C_{0}\) & \(C_{m}\) & \(T\) & \(T_{0}\) \\ \hline \(S_{1}\) & 2 & 1.20 & 94 & 0.05 & 0.52 & 1.5 & 3 \\ \(S_{2}\) & 2 & 1.40 & 70 & 0.04 & 2.40 & 2.4 & 3.5 \\ \(S_{3}\) & 3 & 2.00 & 98 & 0.07 & 1.60 & 3.3 & 3 \\ \(S_{4}\) & 4 & 1.50 & 105 & 0.08 & 0.80 & 3.6 & 4 \\ \(S_{5}\) & 2 & 1.80 & 112 & 1.20 & 1.20 & 2.4 & 2 \\ \(S_{6}\) & 2 & 1.15 & 89 & 1.41 & 1.41 & 2.0 & 3.5 \\ \(S_{7}\) & 3 & 1.64 & 92 & 0.87 & 0.87 & 1.7 & 2.5 \\ \hline \end{tabular} \(S_{i}\) indicates the \(i\)-th subsystem of the equipment.  
\end{table} 
Table 1: Parameters of various components in the system. Figure 6: Nondominated solution set in four simulation experiments. Table 2 shows several plans selected by evaluating the maintenance time, as well as the corresponding maintenance cost, task capability, maintenance time and maintenance schedule of these options. The Gantt chart of the maintenance schedule of Option 1 is shown in Figure 7. It can be seen that the mission satisfied capability of the fleet has a high correlation with the maintenance cost, and the maintenance hours between different schemes are similar after optimizing the maintenance schedule. Figure 8 shows the distribution of the nondominated solution set obtained from the four tests in Figure 6 in terms of the mission satisfied capability dimension. It can be seen that the nondominated solution set obtained by the algorithm proposed in this section is evenly distributed in the target space. The simulation analysis process in the above case analysis is completed based on the matlab platform, running on a PC configured with Intel(R) Core(TM) i7-9750H CPU and Windows 10 operating system.