**2. Quantile-Oriented and Sobol Global Sensitivity Indices**

From a black box perspective, any model may be regarded as a function *R* = g(*X*), where *X* is a vector of *M* uncertain model inputs {*X*1, *X*2,... *XM*}, and *R* is a one-dimensional model output. The uncertain model inputs are considered as statistically independent random variables. This incurs no loss of generality, because mutual relations are created through the computational model on the path to the output.

Three types of global SA (in short SA) are used: *Q* indices, *K* indices and Sobol indices. All three types of SA have the ability to measure sensitivity across the input space (i.e., they are global methods), are capable of dealing with non-linear responses, and can quantify the influence of interactions in a non-additive systems. The first two SAs [62,63] are quantile-oriented, the third is the classical Sobol SA [2,3]. Both quantile-oriented SAs can study structural reliability, the assessment of which is based on limit states and design quantiles. The reason for including Sobol SA is its orientation on variance, which is an important, but not the only, part of reliability analysis.
