**1. Introduction**

The reliability of building structures is influenced by inherent uncertainties associated with the material properties, geometry, and structural load variables to which the reliability measure is sensitive [1]. A common measure of reliability is the failure probability *P<sup>f</sup>* , which is estimated using stochastic models [2]. Failure occurs when the load action is greater than the resistance. In this respect, the key issue is the identification of the significance of input random variables with regard to *P<sup>f</sup>* .

Reliability-oriented sensitivity analysis (ROSA) consists of computing the sensitivity ranking of input variables ranked according to the amount of influence each has on *P<sup>f</sup>* . It is argued that sensitivity analysis (SA) should be used "in tandem" with uncertainty analysis and the latter should precede the former in practical applications [3]. This can encumber the entire computational process, especially in cases of very small *P<sup>f</sup>* .

Alternatively, the assessment of reliability can be performed by comparing the design quantiles of load and resistance [4,5]. A structure is reliable if the design resistance is greater than the design load action. One might ask, if the reliability assessment based on *P<sup>f</sup>* can be replaced by a reliability assessment based on design quantiles, can the SA of *P<sup>f</sup>* be replaced by the SA of design quantiles? For this purpose, new types of sensitivity indices oriented to both design quantiles and *P<sup>f</sup>* can be investigated in engineering applications.

In civil engineering, classical Sobol SA (SSA) [6,7] is applied in the research of structural responses [8–16] or responses in geotechnical applications [17,18]. SSA is attractive for a number of reasons, e.g., it measures sensitivity across the whole input space (i.e., it is a global method), and it is capable of dealing with non-linear responses, as well as measuring the effect of interactions in non-additive models. However, SSA is based on the decomposition of variance of the model output, without a direct reference (only with partial empathy) to reliability [19].

Sobol indices in the context of ROSA can be derived as in [20], by introducing the binary random variable 1 (failure) or 0 (success) as the quantity of interest [21], where the basis of this transformation is the importance measure between *P<sup>f</sup>* and conditional *P<sup>f</sup>* defined in [22]. Indices can be derived in different variants, depending on whether the square of the importance measure [20] or the absolute value of the importance measure [23,24] is considered, but only the variant [20] after Sobol is based on decomposition, with the sum of all indices equal to one.

Both classical Sobol indices [6,7] and Sobol indices in the context of ROSA [20] are a subset of sensitivity indices subordinated to contrasts [25] (in short, Fort contrast indices). The general idea of Fort contrast indices [25] is that the importance of an input variable may vary, depending on what the quantity of interest is. Fort contrast indices define different types of indices based on a common platform, thus providing new perspectives on solving reliability tasks of different types.

It can be shown that Sobol indices in the context of ROSA [20] are Fort contrast indices [25] associated with *P<sup>f</sup>* (referred to as contrast *P<sup>f</sup>* indices in this article). Furthermore, it can be shown that the classical Sobol indices [6,7] are Fort contrast indices [25] associated with variance. In general, the type of Fort contrast index [25] varies, according to the type of contrast used. Contrast functions permit the estimation of various parameters associated with a probability distribution. By changing the contrast, SA can change its key quantity of interest. The contrast may or may not be reliability-oriented.

Fort contrast indices can be considered as global since they are based on changes of the key quantity of interest (*P<sup>f</sup>* , α-quantile, variance, etc.) with regard to the variability of the inputs over their entire distribution ranges and they provide the interaction effect between different input variables. On the other hand, contrast functions account for the variability of the inputs regionally, according to the type of key quantity of interest, e.g., changes around the mean value are important for variance, changes around the quantile are important for the quantile, etc.

Standard [4] establishes the basis that sets out the way in which Eurocodes can be used for structural design. Although the concept of the probability-based assessment of structural reliability has been known about for a long time [5], new types of quantile-oriented SA have not yet been examined, in the context of structural reliability, at an appropriate depth. It can be expected that many of the reliability principles applied in [4] can be applied symmetrically in ROSA using new types of sensitivity indices to find new relationships. The introduced ROSA may be connected to decision-oriented methods [26] in areas of civil engineering, where decision-making under uncertainty is presently uncommon.
