An innovating analysis of the Nataf transformation from the copula viewpoint

This article gives new insight on the Nataf transformation, a widely used tool in reliability analysis. After recalling some basics concerning the copula theory, we explain this transformation in the light of the copula theory and we uncover all the hidden hypothesis made on the dependence structure of the probabilistic model when using this transformation.Some important results concerning dependence modelling are given, such as the risk related to the use of a linear correlation matrix to describe the dependence structure, and the importance of tail dependence in probabilistic modelling for safety assessment. This contribution should allow the reader to be much more aware of the pitfalls in dependence modelling when relying solely on the Nataf transformation.