## 4 Results
### Sensitivity Analysis of the Case Study  
A sensitivity analysis of the solution was conducted concerning the preventive and corrective maintenance costs, with the latter usually being higher due to unplanned downtime expenses. In this case, experiments were carried out considering all combinations of values for \(C_{PM}\) and \(C_{CM}\), ranging from USD 1000 to USD 5000 (in increments of USD 500) and from USD 10,000 to USD 30,000 (in increments of USD 500), respectively.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(k\) & \(c\) & \(T_{j}\) & \(s_{j}\) & \(C_{TOT}(T_{j}s_{j}c)\) & Mean & Std \\ \hline
1 & 4 & 40, 76, 115, 139 & 1.0, 1.0, 1.0, 1.0 & 309.77 \(\times\)\(N\) & 319.18 \(\times\)\(N\) & 5.44 \\ \hline
2 & 5 & 30, 61, 91, 118, 142 & 1.0, 1.0, 1.0, 1.0, 1.0 & 274.21 \(\times\)\(N\) & 284.44 \(\times\)\(N\) & 9.42 \\ \hline
3 & 6 & 22, 43, 71, 94, 121, 154 & 0.7, 1.0, 1.0, 1.0, 1.0, 1.0 & 224.36 \(\times\)\(N\) & 233.73 \(\times\)\(N\) & 6.53 \\ \hline \hline \end{tabular}
\end{table}
Table 16: Optimization results of preventive maintenance times and intervention levels, for a planning horizon of \(N\) = 180 days. Best results achieved in ten model replications, along with the mean and standard deviation (std) of the total cost.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\mathbf{k}\) & **Measure** & \(\lambda\) & \(\beta\) & \(\theta\) \\ \hline \multirow{2}{*}{1} & Mean & 100.0816 & 1.9865 & 0.9690 \\  & \(\varepsilon\) & 0.1176 & 0.0038 & 0.0189 \\ \cline{2-5}  & Mean & 100.4445 & 1.9834 & 1.1862 \\ \cline{2-5}  & \(\varepsilon\) & 0.2237 & 0.0108 & 0.0333 \\ \cline{2-5}  & Mean & 100.7491 & 1.9796 & 1.6559 \\ \cline{2-5}  & \(\varepsilon\) & 0.3356 & 0.0109 & 0.0408 \\ \hline \hline \end{tabular}
\end{table}
Table 15: Model adjustment results.  
The optimal number of preventive maintenance actions was observed for each combination of cost values, as well as the most frequent intervention level for these actions, as shown in Figure 8. It can be observed that the optimal number of preventive maintenance actions, denoted as \(c\), was strongly influenced by variations in the cost of these actions, with these variables being inversely proportional. Therefore, the optimal number of preventive maintenance actions is higher when the cost of these actions is lower, a relationship that becomes more pronounced when corrective costs increase.  
For this example, performing maintenance with a lower level of intervention was considered in a few cases, especially when both preventive and corrective maintenance costs were lower and \(\theta\) was higher (\(k=3\)). However, by reducing the level of intervention,  
Figure 8: Optimal number of maintenance actions and more frequent intervention levels. Results of the case study with \(k=1\), \(2\), and \(3\), regarding parameters \(C_{PM}\) and \(C_{CM}\).  
the preventive maintenance actions needed to be more frequent to achieve the same system improvement factor.  
On the other hand, the impact of corrective maintenance cost on \(c\) was less significant when the difference between \(C_{PM}\) and \(C_{CM}\) was smaller. This is the scenario, for instance, where \(C_{PM}=\) USD 5000 and \(C_{CM}=\) USD 10,000, in which only one preventive maintenance action is indicated.  
Simplified one-dimensional illustrations of these results are shown in Figure 9, with the number of preventive maintenance actions for a few values of \(C_{PM}\) and \(C_{CM}\). Overall, the outcomes for different systems are similar, yet they consistently demonstrate an increasing trend in the number of preventive maintenance actions concerning the parameter \(\theta\), alongside the consideration of preventive maintenance with lower intervention levels, especially for \(k=3\), with lower values of parameters \(C_{PM}\) and \(C_{CM}\).