# Optimization of Inspection Period in Natural Stone Claddings
## 4 Discussion  
The results obtained from the comparison of the optimal solutions for the different maintenance strategies (Figures 4 and 5), more specifically in Figure 4a,d and Figure 5b, may seem contradictory, but they are expected. The optimal solutions with the lowest maintenance costs are the ones with the highest time intervals between inspections, \(t_{\textit{insp}}\), as confirmed in Figure 5a, which relates the design variable with the maintenance costs. If inspections are carried out more frequently (i.e., lower \(t_{\textit{insp}}\)), then there is a greater likelihood of observing the end of the cladding's life earlier, and, consequently, the replacement of the NSC is performed earlier (decreasing the service life), and the number of replacements during the time horizon increases. In this study, it is assumed that the end of the service life is achieved when condition D of degradation is reached. In addition, the decreased period of inspections also contributes to increasing the maintenance costs over time since it will increase the costs associated with the inspection activities. Table 5 shows that as the time interval between inspections decreases, the percentage of the costs associated with  
Figure 7: Comparison of the: (**a**) best optimal solutions of each maintenance strategy; (**b**) worst solutions of each maintenance strategy. inspections increases significantly. For example, for MS1, by comparing with solution S1, the costs associated with the inspections for solution S2 increase by 123%, and for solution S3, the value is approximately 33 times higher. On the other hand, the increase in the costs associated with the maintenance activities varies between 20% and 65%. Similar conclusions can be observed for MS2 and MS3. Other conclusions can be drawn from the direct comparison of the optimal solutions of the three maintenance strategies (Figure 4), which is that it is advantageous to implement strategies with more maintenance activities. For example, for similar maintenance costs, MS3 presents higher service lives, higher efficiency indexes, and a lower number of replacements. This observation is corroborated by the results provided in Figure 7. In Figure 7a,b, the best and the worst optimal solutions of each maintenance strategy are compared, respectively. The results reveal that by balancing the four objective functions, MS3 is the most advantageous maintenance strategy, while MS1 is the least advantageous maintenance strategy. Additionally, from the analysis of the best and worst solutions for each maintenance strategy (Section 3.2), it can be concluded that the time intervals between inspections recommended in the literature are conservative. The literature review (Section 2.1.2) shows that the recommended inspection period to NSC ranges from 2 to 8 years. By comparing these results with the results of the most common value for inspections (5 years) [58], the results reveal that with a low impact on the aesthetic appearance (less than 2%), a considerable reduction in the maintenance costs (ranging between 36% and 58%) can be obtained by increasing the time interval between inspections. Furthermore, the results also reveal that when the period between inspections is increased, the assessment of the degradation condition of NSC is performed later in the cladding's life cycle, thus reducing the number of cleaning actions performed, also postponing the localized repairs. On the one hand, this has economic advantages, increasing the service life of the NSC (decreasing the number of total replacements and increasing the sustainability of NSC) and does not lead to significant differences in the claddings' condition. However, the values provided by the literature review (Section 2.1.2) are deterministic values, defined based on the experience of experts or suggested based on users' requirements.