Propagation of uncertainty through multivariate functions in the framework of sets of probability measures

This paper proposes a solution to Challenge Problem 1 posed by Oberkampf et al. [Reliab. Engng Syst. Safety (this issue)] and focuses on questions of dependence or independence of variables. The specification of uncertainties is consistently reduced to sets of probability measures. For whatever interpretation, the results essentially depend on the choice of combination rule in defining the joint distributions. The approach adopted here is shown to be consistent with interval analysis, random sets and fuzzy sets, and admits a clear description of the influence of the concept of independence used. A MATLAB-tool has been developed that allows to compute the lower and upper probability distributions for all choices of framework and combination rule.