# Optimization of Inspection Period in Natural Stone Claddings
## 4 Discussion
The main advantage of this study is the probabilistic framework of the methodology, which allows encompassing the uncertainty related to the inspection periods, proposing an optimization process to find the most adequate time intervals between inspections. In terms of constraints, as with other probabilistic methodologies, the main limitation of this methodology is the size and quality of the samples. If the sample in which the analysis is based is biased or with influential case studies, the results provided by the methodology will not be realistic. Furthermore, it should be mentioned that the selection of the best maintenance strategy to implement in NSC is a dynamic task. The solution that is adequate for one owner or location/region may not show the same advantages in other places. These decisions are influenced by several factors, such as available budgets, degradation and performance levels, environmental exposure conditions, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Maintenance** & **Optimal** & **Time Interval,** & **Maintenance** & **Costs Associated with** & **Costs associated with** \\
**Strategy** & **Solution** & \(\mathbf{t_{imp}}\) **(Years)** & **Costs (\(\mathbf{\xi}\)/m\({}^{2}\))** & **Inspection (\(\mathbf{\xi}\)/m\({}^{2}\))** & **Maintenance (\(\mathbf{\xi}\)/m\({}^{2}\))** \\ \hline \multirow{4}{*}{MS1} & S1 & 18.8 & 2.54 & 0.52 & 2.02 \\  & S2 & 10.9 & 3.61 & 1.16 & 2.45 \\  & S3 & 1.0 & 20.47 & 17.16 & 3.31 \\ \hline \multirow{4}{*}{MS2} & S4 & 18.8 & 4.32 & 0.52 & 3.8 \\  & S5 & 11.9 & 5.82 & 1.03 & 4.79 \\  & S6 & 1.0 & 23.91 & 16.67 & 7.24 \\ \hline \multirow{4}{*}{MS3} & S7 & 19.0 & 14.58 & 0.51 & 14.07 \\  & S8 & 15.4 & 18.79 & 0.71 & 18.08 \\ \cline{1-1}  & S9 & 1.0 & 74.59 & 17.16 & 57.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of the costs associated with inspection and maintenance activities of the optimal solutions highlighted. users' and owners' perceptions and requirements, local conditions to perform the maintenance works, and the economic and social context of the building, among others. These parameters will influence the degradation process and the impact of the maintenance strategies, and, consequently, different conclusions can be achieved. Therefore, this methodology allows building owners/managers to compare different alternatives and select one that shows a better compromise between the conflicting criteria. For example, let us assume the situation that the owner/manager has a maximum budget of 15.00 \(\upmu\)/m\({}^{2}\) to perform the maintenance works during the time horizon of 150 years. By imposing this constraint, the results reveal that the best solution still belongs to MS3, but the time interval between inspections should be increased from 15 to 20 years (maintenance cost = 13.65 \(\upmu\)/m\({}^{2}\); service life = 275 years; efficiency index = 0.9466; the number of replacements = 0.03). In another situation, where the owner/manager does not want an inspection period higher than 10 years, the results show that the best solution is no longer from MS3 but rather MS2 and has a time interval between inspections of 9 years (maintenance cost = 6.87 \(\upmu\)/m\({}^{2}\); service life = 155 years; efficiency index = 0.9375; the number of replacements = 0.38). Finally, multi-objective optimization is a tool, and the main aim of this study is to show its possibilities when applied to the schedule of inspections in maintenance plans. However, the decision-making behind the schedule of inspections is dependent on several factors. In this study, these four parameters (maintenance cost, service life, efficiency index, and the number of replacements) are chosen, but, depending on the decision maker's requests, other parameters can be evaluated.