# Optimization of Inspection Period in Natural Stone Claddings
## 3 Results
### Analysis of the Best and Worst Solutions for Each Maintenance Strategy  
In order to compare the different optimal solutions for each maintenance strategy, radar charts [60] are used to display the four parameters (objective functions) in a bi-dimensional space and thus analyze the overall influence of each parameter. In Figure 6, for each maintenance strategy, only the three optimal solutions highlighted are plotted in the radar charts, but in the analyses to select the best and the worst solution, all solutions are considered. The optimal solutions highlighted are chosen from all optimal solutions obtained and represent the best, the worst, and an intermediate solution. In the radar charts, the solution with the largest area represents the most advantageous solution. The parameter values for each solution are presented in Table 4.  
In Figure 6a, the optimal solutions highlighted for MS1 are compared. For this maintenance strategy, solution S2 reveals to be the best alternative. This solution presents a time interval between inspections of approximately 11 years and corresponds to a trade-off between the most economical solution (solution S1) and the most expensive one (solution S3). By comparing with solution S1, a slight increase in maintenance costs allows improving the aesthetical appearance and durability of the NSC. On the other hand, solution S3 identifies the least beneficial option for MS1. Although it has the highest efficiency index, the maintenance costs and the impact on users during the time horizon are higher.  
Figure 5: Comparison of the design variable (time interval between inspections, \(t_{\text{insp}}\)) with the four objective functions: (**a**) relationship between maintenance cost and the time interval between inspections; (**b**) relationship between service life and the time interval between inspections; (**c**) relationship between efficiency index and the time interval between inspections; (**d**) relationship between the number of replacements and time interval between inspections.  
Finally, for this maintenance strategy, the time interval between inspections has a limited influence on the service life (approximately 70 years).  
For MS2, the optimal solutions highlighted are shown in Figure 6b. The results reveal that the area for solution S4 is the largest among the three optimal solutions, indicating this solution as the most advantageous option for MS2. Solution S4 presents a time interval between inspections of approximately 19 years and, by slightly sacrificing the aesthetic appearance of the cladding, becomes the most economical solution with longer service life and a lower number of replacements during the time horizon. An inspection period of 19 years for NSC can be considered quite high for some owners/managers of buildings. Therefore, the solution S5, with an approximate time interval between inspections of 12 years, also represents a good alternative. Regarding the least advantageous alternative, this is identified by solution S6.  
Finally, Figure 6c presents the optimal solutions highlighted for MS3. As for MS1, in this maintenance strategy, the results show that the trade-off solution (solution S8) identifies the best alternative, while the most expensive alternative (solution S9) is the least beneficial option. Solution S8 has an approximate time interval between inspections of 15 years, and, by comparing with the most economical solution (solution S7), with a reduction in the durability and slight increase of the maintenance costs, solution S8 maintains the number of replacements and allows improving the aesthetic appearance of the NSC.  
Figure 6: Comparison of the optimal solutions for: (**a**) maintenance strategy 1; (**b**) maintenance strategy 2; (**c**) maintenance strategy 3.