System reliability under prescribed marginals and correlations: Are we correct about the effect of correlations?

Many reliability problems involve correlated random variables. However, the probabilistic specification of random variables is commonly given in terms of marginals and correlations, which is actually incomplete because the data dependency needed for distribution modeling is not characterized. The implicitly assumed Gaussian dependence structure is not necessarily true and may bias the reliability result. To investigate the effect of correlations on system reliability under non-Gaussian dependence structures, a general approach to the probability distribution model construction based on the pair-copula decomposition is proposed. Numerical examples have highlighted the importance of dependence modeling in system reliability since large deviation in failure probabilities under different dependencies is observed. The method for identifying the best fit data dependency from data is later provided and illustrated with a retaining wall. It is demonstrated that the reliability result can be accurately estimated if the qualitative dependence structure is complemented to the available quantitative statistical information.