Numerical accuracy and efficiency in the propagation of epistemic and aleatory uncertainties

The need to differentiate between epistemic and aleatory uncertainty is now well admitted by the risk analysis community. One way to do so is to model aleatory uncertainty by classical probability distributions and epistemic uncertainty by means of possibility distributions, and then propagate them by their respective calculus. The result of this propagation is a random fuzzy variable. When dealing with complex models, the computational cost of such a propagation quickly becomes too high. In this paper, we propose a numerical approach, the RaFu method, whose aim is to determine an optimal numerical strategy so that computational costs are reduced to their minimum, while using the theoretical framework mentioned above. We also give some means to take account of the resulting numerical error. The benefits of the RaFu method are shown by comparisons with previous methodologies.