# Towards Optimizing Multi-Level Selective Maintenance via Machine Learning Predictive Models
## 5 Numerical Results
### Results  
By exploiting the ANN model, we predict, firstly, the degradation factor \(b_{i}(k_{i},m)\) at every breakdown \(\sigma_{m}\) (\(\sigma_{m}=1,2,\ldots,7\)) for each component (\(i=1,2,\ldots,9\)). Then, based on experiment results and utilizing Equation (24), we establish the actual age \(\gamma_{i}^{*}(k_{i},1)\) for each component. These results are illustrated in Table 4. We observe a slight degradation in the components at the end of the first mission (\(b_{i}(k_{i},1)\leq 0.06\)), and this increases with subsequent missions. Note that the results obtained in Table 4 are raw, i.e., without the implementation of maintenance strategies and optimization model at each break. Indeed, our predictive model updates these parameters after each maintenance plan adopted during a given break. The EDA approach on MATLAB 2022 software to address the challenge of proposing a maintenance plan that minimizes costs under reliability and time constraints by using the results of ANN-based predictive model generates the solutions presented in Table 5. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \(\mathbf{C_{1}}\) & \(\mathbf{C_{2}}\) & \(\mathbf{C_{3}}\) & \(\mathbf{C_{4}}\) & \(\mathbf{C_{5}}\) & \(\mathbf{C_{6}}\) & \(\mathbf{C_{7}}\) & \(\mathbf{C_{8}}\) & \(\mathbf{C_{9}}\) \\ \hline \(\gamma_{1}^{*}(\mathbf{k_{i}}\mathbf{1})\) & 127 & 131 & 126 & 126 & 119 & 121 & 120 & 130 & 131 \\ \(b_{1}(k_{i}\mathbf{1})\) & 0.07 & 0.07 & 0.07 & 0.13 & 0.06 & 0.07 & 0.07 & 0.06 \\ \(\gamma_{1}^{*}(\mathbf{k_{i}}\mathbf{2})\) & 115 & 120 & 115 & 115 & 108 & 110 & 109 & 119 & 120 \\ \(b_{1}(k_{i}\mathbf{2})\) & 0.17 & 0.15 & 0.16 & 0.16 & 0.22 & 0.15 & 0.17 & 0.16 & 0.15 \\ \(\gamma_{1}^{*}(k_{i}\mathbf{2})\) & 102 & 107 & 102 & 102 & 95 & 97 & 96 & 106 & 107 \\ \(b_{1}(k_{i}\mathbf{3})\) & 0.29 & 0.27 & 0.28 & 0.28 & 0.35 & 0.28 & 0.30 & 0.27 & 0.26 \\ \(\gamma_{1}^{*}(k_{i}\mathbf{4})\) & 80 & 84 & 79 & 79 & 72 & 74 & 73 & 83 & 84 \\ \(b_{1}(k_{i}\mathbf{4})\) & 0.53 & 0.51 & 0.54 & 0.54 & 0.63 & 0.55 & 0.57 & 0.52 & 0.50 \\ \(\gamma_{1}^{*}(k_{i}\mathbf{5})\) & 72 & 71 & 66 & 66 & 66 & 81 & 60 & 100 & 71 \\ \(b_{1}(k_{i}\mathbf{5})\) & 0.64 & 0.68 & 0.72 & 0.72 & 0.72 & 0.46 & 0.77 & 0.33 & 0.67 \\ \(\gamma_{1}^{*}(k_{i}\mathbf{6})\) & 65 & 63 & 58 & 69 & 81 & 83 & 52 & 82 & 63 \\ \(b_{1}(k_{i}\mathbf{6})\) & 0.74 & 0.80 & 0.84 & 0.67 & 0.51 & 0.43 & 0.91 & 0.53 & 0.79 \\ \(\gamma_{1}^{*}(k_{i}\mathbf{7})\) & 65 & 47 & 32 & 59 & 77 & 87 & 26 & 96 & 47 \\ \(b_{1}(k_{i}\mathbf{7})\) & 0.74 & 0.90 & 0.95 & 0.83 & 0.56 & 0.39 & 0.91 & 0.37 & 0.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The obtained actual age and degradation factor for each component \(i\) at the end mission \(m\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(i\) & \(\mathbf{A_{i}^{*}}\) & \(\mathbf{k_{i}}\) & \(\mathbf{\xi(k_{i})}\) & \(\mathbf{C(k_{i})}\) & \(\mathbf{d(k_{i})}\) \\  & (\(\mathbf{t.u}\)) & & (\(\mathbf{t.u}\)) & (\(\mathbf{m.u}\)) & (\(\mathbf{t.u}\)) \\ \hline \multirow{4}{*}{\(\mathbf{C_{7}}\)} & \multirow{4}{*}{129} & 1 & 0 & 0 & 0 \\ \cline{3-6}  & & 2 & +10 & 13 & 3 \\ \cline{3-6}  & & 3 & +15 & 18 & 4 \\ \cline{3-6}  & & 4 & +20 & 25 & 6 \\ \cline{3-6}  & & 5 & Replacement & 35 & 8 \\ \hline \multirow{4}{*}{\(\mathbf{C_{8}}\)} & \multirow{4}{*}{139} & 1 & 0 & 0 & 0 \\ \cline{3-6}  & & 2 & +3 & 7 & 5 \\ \cline{3-6}  & & 3 & +15 & 15 & 6 \\ \cline{3-6}  & & 4 & +30 & 26 & 7 \\ \cline{3-6}  & & 5 & Replacement & 30 & 10 \\ \hline \multirow{4}{*}{\(\mathbf{C_{9}}\)} & \multirow{4}{*}{140} & 1 & 0 & 0 & 0 \\ \cline{3-6}  & & 2 & +10 & 10 & 2 \\ \cline{3-6}  & & 3 & +36 & 25 & 5 \\ \cline{3-6}  & & 4 & +41 & 30 & 7 \\ \cline{3-6}  & & 5 & Replacement & 40 & 9 \\ \hline \hline \end{tabular}
\end{table}