**7. Conclusions**

Low and high quantiles represent a significant part of the analysis of reliability, not only in the design of building structures. The sensitivity analysis of the resistance *R* of the steel strut showed significant similarities and differences between both types of quantile-oriented sensitivity analysis (SA) and classical Sobol SA.

The quantile deviation *l* was defined as the difference between superquantile and subquantile. New global sensitivity measures based on the quantile deviation *l* of model output were introduced. The quantile deviation *l* measures the statistical variability around the quantile similarly to how standard deviation measures the statistical variability around the mean value. By using *l* to the first power, it is possible to rewrite quantile-oriented sensitivity indices subordinated to contrasts (*Q* indices) in a new form. The obtained results of the presented case study established that *Q* indices are the least comprehensible because they exhibit the strongest interaction effects between inputs. The results of Sobol SA are clear; however, they are not directly oriented to design quantiles and reliability.

With this motivation in mind, new quantile-oriented sensitivity indices (*K* indices) are expressed in this paper with sensitivity measure *l* 2 expressed in the same unit as variance, thus approaching Sobol sensitivity indices with their properties. *l* <sup>2</sup> has a significance similar to variance, but around quantile. The unit consistency between *K* indices and Sobol indices makes *K* indices attractive in stochastic models, where more parameters (goals) of the probability distribution of the model output need to be analysed. Overall, the new *K* indices can be considered effective in solving the effect of input random variables on design quantiles.

The case study based on a non-linear and non-monotonic function showed that all three types of SA give very similar conclusions when total indices are evaluated. Although Sobol SA is based on the decomposition of only the variance of the model output, its conclusions are in good agreement with the conclusions of both quantile-oriented SA. The case study showed that the correlation between quantile deviation *l* and standard deviation *σ<sup>R</sup>* may or may not be strong. Although *l* correlates with *σR*, *l* is also related to the shape of the probability distribution.

In general, it is always better to prioritize quantile-oriented types of global SA, which measure the statistical variability around a quantile (e.g., quantile deviation *l*) rather than around a mean value (variance), for quantile-based reliability analysis.

**Funding:** The work has been supported and prepared within the project namely "Probability oriented global sensitivity measures of structural reliability" of The Czech Science Foundation (GACR, https://gacr.cz/) no. 20-01734S, Czechia.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The author declares no conflict of interest.
