## 4 Results
### Numerical Examples
Additionally, this example only considered preventive maintenance with intervention levels of 100%, which means that the optimization algorithm needed to define only the optimal times to perform the maintenance activities. The respective results are presented in Table 12.  
For the fourth case example, the experiments considered four equivalent systems subject to PMA intervention levels of 50% or 100%. The results are presented in Table 13.  
It is noteworthy that in all simulated scenarios, the proposed approach indicated a PM planning with a single maintenance activity over the time horizon. This result persisted even with changes in the corrective and preventive maintenance costs, as shown in Figure 5, for the first case example. It was observed that an increase in corrective maintenance costs caused an anticipation of the maintenance activity to reduce the total cost, but the impact was relatively small. This result is because the failure intensity function tended to have a constant value over time in the examples, according to Figure 1. Under this condition, the improvement promoted by MP was relatively small, independent of the intervention \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Replication** & \(\lambda\) & \(\beta\) & \(\theta\) & \(\epsilon\) & \(T_{j}\) & \(s_{j}\) & \(C_{\text{TOT}}\)**(\(T_{j}\)\(\mathbf{s_{j}}\)\(\mathbf{c}\))** \\ \hline \#1 & 843.3548 & 1.8067 & 2.9728 & 1 & 348 & 0.5 & \(\mathbf{29.85}\times N\) \\ \#2 & 836.6138 & 1.8040 & 2.9818 & 1 & 347 & 0.5 & \(30.16\times N\) \\ \#3 & 835.1684 & 1.7999 & 2.9952 & 1 & 348 & 0.5 & \(30.27\times N\) \\ \#4 & 835.9370 & 1.8063 & 2.9922 & 1 & 347 & 0.5 & \(30.14\times N\) \\ \#5 & 838.6593 & 1.8007 & 2.9894 & 1 & 347 & 0.5 & \(30.12\times N\) \\ \#6 & 833.4663 & 1.8056 & 2.9937 & 1 & 347 & 0.5 & \(30.26\times N\) \\ \#7 & 838.8566 & 1.8049 & 2.9937 & 1 & 348 & 0.5 & \(30.04\times N\) \\ \hline \hline \end{tabular}
\end{table} 
Table 13: _Cont._ \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Replication** & \(\lambda\) & \(\beta\) & \(\theta\) & \(\epsilon\) & \(T_{j}\) & \(s_{j}\) & \(C_{\text{TOT}}\)**(\(T_{j}\)\(\mathbf{s_{j}}\)\(\mathbf{c}\))** \\ \hline \#1 & 1148.0923 & 1.9924 & 0.0118 & 1 & 373 & 1.00 & \(42.72\times N\) \\ \#2 & 1157.0846 & 1.9963 & 0.0022 & 1 & 391 & 1.00 & \(42.41\times N\) \\ \#3 & 1142.0265 & 1.9916 & 0.0391 & 1 & 372 & 1.00 & \(42.77\times N\) \\ \#4 & 1155.7233 & 1.9962 & 0.0111 & 1 & 374 & 1.00 & \(42.37\times N\) \\ \#5 & 1140.5708 & 1.9867 & 0.0384 & 1 & 328 & 1.00 & \(43.03\times N\) \\ \#6 & 1139.0892 & 1.9956 & 0.0000 & 1 & 369 & 1.00 & \(43.29\times N\) \\ \#7 & 1185.0730 & 1.9990 & 0.0325 & 1 & 386 & 1.00 & \(\mathbf{40.81}\times N\) \\ \#8 & 1146.1480 & 1.9998 & 0.0357 & 1 & 375 & 1.00 & \(42.61\times N\) \\ \#9 & 1129.0687 & 1.9951 & 0.0591 & 1 & 387 & 1.00 & \(43.25\times N\) \\ \#10 & 1149.6619 & 1.9938 & 0.0216 & 1 & 374 & 1.00 & \(42.56\times N\) \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c c c c} \hline \hline
**mean** & 1149.3829 & 1.9949 & 0.0266 & 1 & 372.9 & 1.00 & \(42.57\times N\) \\ \(\epsilon\) & 9.8835 & 0.0024 & 0.0121 & 0 & 11.5 & 0.00 & \(0.46\) \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Optimal results of the third case example. Bold value represents the best result. level, and did not significantly affect the total maintenance cost. When the preventive maintenance has minimal impact on extending the component or system's lifespan, conducting regular maintenance becomes less efficient, especially if the maintenance cost outweighs the benefits gained. On the other hand, the cost of preventive maintenance has a higher impact on the maintenance time, and higher costs extend the maintenance action. This characteristic can be better observed in Figure 6.  
In general, maintenance activities with an intervention level of 20% were indicated in most cases. However, more comprehensive maintenance activities were indicated in cases where the times of such activities were small.