## 4 Results
### Numerical Examples
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Replication** & \(c\) & \(T_{j}\) & \(s_{j}\) & \(C_{\text{TOT}}(T_{j}s_{j}\mathbf{c})\) \\ \hline \#1 & 1 & 48 & 0.9 & **847.15**\(\times N\) \\ \#2 & 1 & 40 & 0.9 & 1127.42 \(\times N\) \\ \#3 & 1 & 41 & 0.9 & 1030.22 \(\times N\) \\ \#4 & 1 & 38 & 0.9 & 1228.06 \(\times N\) \\ \#5 & 1 & 38 & 0.9 & 1243.24 \(\times N\) \\ \#6 & 1 & 44 & 0.5 & 938.48 \(\times N\) \\ \#7 & 1 & 38 & 0.9 & 1199.41 \(\times N\) \\ \#8 & 1 & 28 & 0.5 & 1163.03 \(\times N\) \\ \#9 & 1 & 45 & 0.9 & 884.87 \(\times N\) \\ \#10 & 1 & 39 & 0.9 & 1220.14 \(\times N\) \\ \hline Mean & 1 & 39.90 & 0.82 & 1088.20 \(\times N\) \\ \(\varepsilon\) & 0 & 3.35 & 0.10 & 93.71 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Results of the first case example, with PM cost independent of the intervention level. Planning horizon of \(N=24\) months (730 days). Bold value represents the best result. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Replication** & \(c\) & \(T_{1}\) & \(s_{1}\) & \(C_{\text{TOT}}(T_{1}s_{1}\mathbf{c})\) \\ \hline \#1 & 1 & 39 & 0.2 & 913.66 \(\times N\) \\ \#2 & 1 & 60 & 0.2 & 790.27 \(\times N\) \\ \#3 & 1 & 33 & 0.2 & 1036.27 \(\times N\) \\ \#4 & 1 & 30 & 0.2 & 1170.97\(\times N\) \\ \#5 & 1 & 34 & 0.2 & 1146.51 \(\times N\) \\ \#6 & 1 & 24 & 0.2 & 993.19 \(\times N\) \\ \#7 & 1 & 32 & 0.2 & 1145.47 \(\times N\) \\ \#8 & 1 & 31 & 0.2 & 975.67 \(\times N\) \\ \#9 & 1 & 35 & 0.2 & **817.29**\(\times N\) \\ \#10 & 1 & 31 & 0.2 & 1162.41 \(\times N\) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Maintenance optimization results for the first case example. The value in bold indicates the best solution obtained in 10 replications. Planning horizon of \(N=24\) months (730 days). The 90% intervention level solution obtained in Replication 1 is the one that presented the lowest total cost. In general, the total costs are slightly higher than in the previous case, as the fixed cost of USD 4000 is higher than the cost of a 20% intervention level. The results of the second case example are presented in Table 11. Again, the results of the intervention level and total maintenance cost are quite consistent. The system indicates a single preventive maintenance action around the day T = 140 and an intervention level of 20%. For the third case example, an \(N\) = 48-month planning horizon was considered for two observed systems. It is important to note that, in this case, the joining of the two systems' \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Replication** & \(\lambda\) & \(\beta\) & \(\theta\) & \(c\) & \(T_{j}\) & \(s_{j}\) & \(C_{\text{TOT}}\)(\(T_{j}\)s\({}_{j}\),c) \\ \hline \#1 & 1140.0614 & 1.5543 & 0.1355 & 1 & 140 & 0.2 & 19.98 \(\times\)\(N\) \\ \#2 & 1176.7846 & 1.5365 & 0.0087 & 1 & 140 & 0.2 & 19.71 \(\times\)\(N\) \\ \#3 & 1173.6136 & 1.5464 & 0.0295 & 1 & 141 & 0.2 & 19.61 \(\times\)\(N\) \\ \#4 & 1189.1688 & 1.5465 & 0.0049 & 1 & 140 & 0.2 & 19.35 \(\times\)\(N\) \\ \#5 & 1133.3206 & 1.4970 & 0.0013 & 1 & 152 & 0.2 & 21.18 \(\times\)\(N\) \\ \#6 & 1204.0306 & 1.5654 & 0.0022 & 1 & 143 & 0.2 & 18.84 \(\times\)\(N\) \\ \#7 & 1195.5719 & 1.5634 & 0.0001 & 1 & 141 & 0.2 & 19.03 \(\times\)\(N\) \\ \#8 & 1231.2843 & 1.5971 & 0.0140 & 1 & 145 & 0.2 & **17.95**\(\times\)\(N\) \\ \#9 & 1180.0496 & 1.5407 & 0.0118 & 1 & 144 & 0.2 & 19.59 \(\times\)\(N\) \\ \#10 & 1194.1564 & 1.5550 & 0.0023 & 1 & 118 & 0.2 & 19.26 \(\times\)\(N\) \\ \hline mean & 1181.8042 & 1.5502 & 0.0210 & 1 & 140.4 & 0.2 & 19.45 \(\times\)\(N\) \\ \(\varepsilon\) & 17.9246 & 0.0157 & 0.0255 & 0 & 5.38 & 0 & 0.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Optimal results of the second case example. Planning horizon of \(N\) = 24 months (730 days). Bold value represents the best result. Figure 4: Expected number of failures in function of the intervention level. Example for three PM cycles with times T = [200, 400, 600] and end of operation at t = 730 days. data made it possible to consider the first system for which there was no failure data in the period.