Dependence modelling with copula in probabilistic studies, a practical approach based on numerical experiments

Taking into account the stochastic dependence between sources of uncertainties is of uttermost importance in reliability studies. Most of the time, the practitioner has a handful of scalars measuring correlations between these sources, and he is faced to the challenge of describing the dependence structure based on this information. In this communication, we show that this approach might be irrelevant in the general case, but may be improved with some additional work. In the first section, we show that the use of the linear correlation coefficient should be avoided as a general way to represent stochastic dependence. We introduce the notion of copula as the most exhaustive representation of stochastic dependence, then we define the notion of measure of association. We confirm that the linear correlation is not such a measure, and we present three such measures (Spearman's rho, Kendall's tau and coefficients of tail dependence) that can be viewed as replacements of the usual linear correlation data. Then, in the context of an aeronautic application dedicated to the risks induced by the use of electronic protable devices during a flight, we perform a numerical experiment in order to check within which bounds we can rely on measure of association for the description of the stochastic dependence. The conclusion aims at giving some experimental guidelines for stochastic modelling based on such measures.