# Towards Optimizing Multi-Level Selective Maintenance via Machine Learning Predictive Models
## 5 Numerical Results
### Results

Table 3: _Cont._As shown in the table, the actual predicted age of the components is quite high after performing the three first missions (until \(\sigma_{3}\)), so the best maintenance strategy selected for the nine components during the breaks \(\sigma_{1}\), \(\sigma_{2}\) and \(\sigma_{3}\) is \(\approx\) 111 111 111 \(\approx\), which means doing nothing for all components (\(k_{i}=1\), \(i=1,\ldots,9\)). After accomplishing the fourth mission (\(\sigma_{4}\)), some components are deteriorated and, consequently, the reliability system decreases. By minimizing the total maintenance cost under reliability and time constraints, the best maintenance policy recommended involves implementing strategy 2 on component 1 (\(k_{1}=2\)), strategy 2 on component 5 (\(k_{5}=2\)), strategy 3 on component 6 (\(k_{6}=3\)), strategy 3 on component 8 (\(k_{8}=3\)), and employing strategy 1 for the remaining components. Following this multi-level maintenance plan, the age of component 1 is increased by 10 \(t.u\) (time units), and component 5 is increased by 7 \(t.u\), component 6 by 20 \(t.u\), component 8 by 15 \(t.u\), while no action is performed on the other components. The optimal policy results in a total maintenance cost of 116 \(m.u\) (monetary units), a total maintenance time of 13 \(t.u\), and aims to achieve a reliability value equal to 0.9078. The obtained maintenance plan during the considered operating time shows that the system reliability decreases during each mission. In order to maintain the system reliability higher than 0.9, the maintenance action selected at the end of the mission allows us to increase the component's actual age as well as the reliability system; this increase is presented in Figure 7 by an increasing line. Otherwise, the system reliability follows an exponential variation during the operating time. As shown in Figure 7, the maintenance action suggested by the proposed approach during the intermission break ensures that the system's reliability respects the set threshold until the end of the mission. \begin{table}
\begin{tabular}{c c c c c c} \hline \(\sigma_{m}\) & Maintenance Plan & \(k_{i}\) & \(MC(k_{i}\),\(m\)) & \(d(k_{i})\) & \(R(\gamma^{*}(k_{i}\),\(m\)+1)) \\ \hline \(\sigma_{1}\) & \(\ast\) 111 111 11\(\approx\) & \begin{tabular}{c} _Do nothing_ \\ (\(k_{i}=1\)) \\ \end{tabular} & 0 & 0 & 0.9898 \\ \(\sigma_{2}\) & \(\ast\) 111 111 11\(\approx\) & \begin{tabular}{c} _Do nothing_ \\ (\(k_{i}=1\)) \\ \end{tabular} & 0 & 0 & 0.9868 \\ \(\sigma_{3}\) & \(\ast\) 111 111 1\(\approx\) & \
\begin{tabular}{c} _Do nothing_ \\ (\(k_{i}=1\)) \\ \end{tabular} & 0 & 0 & 0.9868 \\ \(\sigma_{4}\) & \(\ast\) 211 123 131 \(\approx\) &
\begin{tabular}{c} _C_{5} : \(k_{5}=2\) \\ \(C_{6}:k_{6}=3\) \\ \(C_{8}:k_{8}=3\) \\ \(C_{1}:k_{1}=3\) \\ \(C_{2}:k_{2}=2\) \\ \(C_{4}:k_{4}=2\) \\ \(C_{6}:k_{8}=4\) \\ \(C_{7}:k_{8}=4\) \\ \(C_{8}:k_{8}=4\) \\ \(C_{9}:k_{9}=2\) \\ \(C_{1}:k_{1}=3\) \\ \(C_{4}:k_{4}=2\) \\ \(C_{5}:k_{5}=3\) \\ \(C_{6}:k_{6}=3\) \\ \(C_{8}:k_{8}=4\) \\ \(C_{1}:k_{1}=5\) \\ \(C_{2}:k_{2}=2\) \\ \(C_{4}:k_{4}=3\) \\ \(C_{5}:k_{5}=2\) \\ \(C_{6}:k_{6}=3\) \\ \hline \end{tabular}
\end{table} 
Table 5: The multi-level maintenance plan obtained for the required reliability level (0.9).