## 3 Results
Table 5 presents the results of unavailability by scenario, and the reduction of inefficiency, measured as the percentual difference between the system unavailability reported from the initial solution with null tolerance factor (i.e., tentative execution plan), and the unavailability reported by the optimal solution. As observed in the previous results, the reduction of inefficiency through the application of the framework increases progressively as the tolerance factor increases, achieving a reduction of 26% in the downtime of the system under a 5% tolerance factor, reducing unavailability from eight weeks to six weeks. Additionally, what is observed is a decrease in the progressive reduction of inefficiency by consecutively reaching a higher tolerance factor. For example, going from 2% to 3% in the increase of the allowable tolerance causes an increase of almost 6% in the reduction of inefficiency, while going from 4% to 5% only reports a 0.2% in the reduction of unavailability. The use of the tolerance time windows, as well as the assignment of the execution times and conformed grouping schemes, can be presented employing a Gantt chart-based representation, according to the nomenclature presented in Figure 3. Figure 7 represents the base PM plan of the critical activities analyzed for a planning horizon of 52 weeks. As observed, system stoppages are represented by grey vertical lines, while system unavailability is represented by green bars. The initial tentative maintenance plan includes a total of 35 stoppages, generating system unavailability of approximately 8 weeks per year. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Tolerance Factor (\(e\))** & **Best Value** & **Optimality** & **Resolution** & **A\({}^{\text{AV}}\) (\%)** & **D\({}^{\text{AV}}\) (\%)** & \(f^{\text{A}}\) (\%)** & \(f^{\text{D}}\) (\%) & \(f^{\text{D}}\) (\%) \\ \hline
0.00 & 7.98 & 0 & 0 & 0 & 0 & 0 & 100 \\
1.00 & 7.59 & 0 & 0.1327 & 11.20 & 27.79 & 39.53 & 37.91 & 32.56 \\
2.00 & 7.45 & 0 & 0.3022 & 10.57 & 32.15 & 44.18 & 30.23 & 25.58 \\
3.00 & 6.87 & 0 & 0.3352 & 21.58 & 18.74 & 32.56 & 46.51 & 20.93 \\
4.00 & 5.89 & 0 & 0.6390 & 35.87 & 12.04 & 23.25 & 55.81 & 20.93 \\
5.00 & 5.87 & 0 & 0.9753 & 20.78 & 26.92 & 37.21 & 46.51 & 16.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance indicators for instances under several tolerance factors. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Tolerance Factor (\(e\)) (\%)** & **System Unavailability** & **Inefficiency Reduction (\%)** \\ \hline
0.00 & 7.98 & - \\
1.00 & 7.59 & 4.6 \\
2.00 & 7.45 & 6.6 \\
3.00 & 6.87 & 13.9 \\
4.00 & 5.89 & 26.2 \\
5.00 & 5.87 & 26.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of unavailability of the system and reduction of inefficiency, for different tolerance factors. If the application of a tolerance factor of 5% is now considered, then the number of stoppages is reduced to 19, which implies an inefficiency reduction of almost 30%, compared to the base case, which offers a gain equivalent of two-week system availability per year. What is observed in this scenario (See Figure 8) is the use of the time-window tolerances for the generation of grouping schemes, thus allowing to considerably reduce the number of interruptions while increasing the availability of the system. Figure 7: Optimal grouping schemes for the case study under tolerance factor \(e=0\%\), considering a 52-week planning horizon. (**a**) First semester (weeks 1–26); (**b**) Second semester (weeks 27–52).