When dealing with engineering systems subject to uncertainty, identifying which parameters most influence the response of the system is an important step. It is often referred to as sensitivity analysis and is typically conducted at an early stage of a project. Modelling uncertainty and dependence between variables is usually done by introducing a random vector X = (X_1, ..., X_d) as input data. The effect of each random vector component on the system is then expressed in terms of sensitivity indices, which can be calculated in several ways. Among them, Sobol' and Kucherenko indices for uncorrelated and correlated random vectors, respectively, are most commonly used. In this contribution, we propose a benchmark study consisting of three structural and three geotechnical problems, including one using the finite element method. In a first step, we compute the total-effect index of each component of the random vector X. Then, after sorting the components according to their corresponding index in ascending order, we successively reduce components by keeping only the most impacting ones so that the number of components will evolve as d, d-1, ..., 1. The cancelled components are set to their corresponding expected values. The goal is finally to quantify the influence of reduced random vectors on the mean value and the variance of the model, as well as the variation of the probability of failure of the system. As finite element models are used, the failure probability is estimated via active learning reliability and Monte Carlo simulations.