# Towards Optimizing Multi-Level Selective Maintenance via Machine Learning Predictive Models
## 5 Numerical Results
### FMS Study Case and Input Data  
The Flexible Manufacturing System situated in the Laboratory of Computer Engineering, Production, and Maintenance (LGIPM) serves the dual purpose of research and teaching. We assume that the specific maintenance periods throughout the year align with five educational breaks, as illustrated in Figure 5. The selection of the number of maintenance actions is primarily influenced by the availability of service technicians. As a result, a multi-level selective maintenance approach is highly recommended for the FMS during each scheduled downtime.  
Given the extensive array of components in the FMS, encompassing electrical, electronic, and mechanical elements totaling around 300,000, we have opted to focus on a multi-series parallel subsystem. This subsystem of the FMS consists of nine components (\(n=9\)), as shown in Figure 6, and serves as the basis for developing our proposed methodology.  
As explained through this paper, we adopt multi-level selective maintenance in which each level proportionally improves the component's age \(\zeta(k_{i})\) compared to its value before maintenance activity as well as its reliability. In addition, each level \(k_{i}\) is characterized by its  
Figure 5: The missions and breakdowns of FMS.  
Figure 6: The FMS structure.  
cost and time duration, as detailed in Table 3. The theoretical age given by the manufacturer (\(A_{i}^{*}\)) for each component is defined in the second column. Note that, for the illustrative example, we have opted for a choice among five maintenance levels, starting from the first level (\(k_{i}=1\)), which involves no action, to the final level (\(k_{i}=5\)), which includes the replacement of the component. At each breakdown, the maintenance plan must ensure the fulfillment of the subsequent mission with a reliability level exceeding or equal to 90% (\(R^{*}=0.9\)).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(i\) & \(A_{i}^{*}\) & \(k_{i}\) & \(\zeta(k_{i})\) & \(C(k_{i})\) & \(d(k_{i})\) \\  & (\(t.u\)) & & (\(t.u\)) & (\(m.u\)) & (\(t.u\)) \\ \hline \multirow{4}{*}{\(C_{1}\)} & \multirow{4}{*}{136} & 1 & 0 & 0 & 0 \\ \cline{3-6}  & & 2 & +5 & 5 & 2 \\ \cline{3-6}  & & 3 & +17 & 12 & 3 \\ \cline{3-6}  & & 4 & +30 & 16 & 5 \\ \cline{3-6}  & & 5 & Replacement & 22 & 7 \\ \hline \multirow{4}{*}{\(C_{2}\)} & \multirow{4}{*}{140} & 1 & 0 & 0 & 0 \\ \cline{3-6}  & & 2 & +10 & 17 & 4 \\ \cline{3-6}  & & 3 & +15 & 20 & 5 \\ \cline{3-6}  & & 4 & +22 & 27 & 7 \\ \cline{3-6}  & & 5 & Replacement & 36 & 9 \\ \hline \multirow{4}{*}{\(C_{3}\)} & \multirow{4}{*}{135} & 1 & 0 & 0 & 0 \\ \cline{3-6}  & & 2 & +6 & 10 & 5 \\ \cline{3-6}  & & 3 & +19 & 12 & 8 \\ \cline{3-6}  & & 4 & +21 & 15 & 10 \\ \cline{3-6}  & & 5 & Replacement & 18 & 12 \\ \hline \multirow{4}{*}{\(C_{4}\)} & \multirow{4}{*}{135} & 1 & 0 & 0 & 0 \\ \cline{3-6}  & & 2 & +6 & 8 & 5 \\ \cline{3-6}  & & 3 & +19 & 15 & 8 \\ \cline{3-6}  & & 4 & +21 & 25 & 10 \\ \cline{3-6}  & & 5 & Replacement & 34 & 12 \\ \hline \multirow{4}{*}{\(C_{5}\)} & \multirow{4}{*}{128} & 1 & 0 & 0 & 0 \\ \cline{3-6}  & & 2 & +7 & 6 & 1 \\ \cline{3-6}  & & 3 & +12 & 12 & 3 \\ \cline{3-6}  & & 4 & +25 & 17 & 6 \\ \cline{3-6}  & & 5 & Replacement & 26 & 8 \\ \hline \multirow{4}{*}{\(C_{6}\)} & \multirow{4}{*}{130} & 1 & 0 & 0 & 0 \\ \cline{3-6}  & & 2 & +5 & 12 & 2 \\ \cline{3-6}  & & 3 & +20 & 15 & 4 \\ \cline{3-6}  & & 4 & +25 & 28 & 6 \\ \cline{3-6}  & & 5 & Replacement & 35 & 8 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameters of multi-level maintenance for each component.