*Article* **Global Sensitivity Analysis of Quantiles: New Importance Measure Based on Superquantiles and Subquantiles**

**Zdenˇek Kala**

**Citation:** Kala, Z. Global Sensitivity Analysis of Quantiles: New Importance Measure Based on Superquantiles and Subquantiles. *Symmetry* **2021**, *13*, 263. https:// doi.org/10.3390/sym13020263

Academic Editors: Edmundas Kazimieras Zavadskas, Jurgita Antucheviˇciene and ˙ Zenonas Turskis Received: 21 January 2021 Accepted: 31 January 2021 Published: 4 February 2021

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Department of Structural Mechanics, Faculty of Civil Engineering, Brno University of Technology, 602 00 Brno, Czech Republic; kala.z@fce.vutbr.cz

**Abstract:** The article introduces quantile deviation *l* as a new sensitivity measure based on the difference between superquantile and subquantile. New global sensitivity indices based on the square of *l* are presented. The proposed sensitivity indices are compared with quantile-oriented sensitivity indices subordinated to contrasts and classical Sobol sensitivity indices. The comparison is performed in a case study using a non-linear mathematical function, the output of which represents the elastic resistance of a slender steel member under compression. The steel member has random imperfections that reduce its load-carrying capacity. The member length is a deterministic parameter that significantly changes the sensitivity of the output resistance to the random effects of input imperfections. The comparison of the results of three types of global sensitivity analyses shows the rationality of the new quantile-oriented sensitivity indices, which have good properties similar to classical Sobol indices. Sensitivity indices subordinated to contrasts are the least comprehensible because they exhibit the strongest interaction effects between inputs. However, using total indices, all three types of sensitivity analyses lead to approximately the same conclusions. The similarity of the results of two quantile-oriented and Sobol sensitivity analysis confirms that Sobol sensitivity analysis is empathetic to the structural reliability and that the variance is one of the important characteristics significantly influencing the low quantile of resistance.

**Keywords:** sensitivity analysis; buckling; reliability; safety; quantile; superquantile; subquantile; civil engineering; limit states
