Multivariate models of uncertainty: A local random set approach

This article is devoted to the construction of random sets from variability intervals and non-parametric inference. At fixed confidence level, local random sets are defined whose aggregation admits the calculation of upper probabilities of events. In the multivariate case, a number of ways of combination is highlighted and the corresponding upper probabilities are computed. This way non-parametric upper estimates of the distribution of limit state functions of structures as well as upper failure probabilities are derived. The method is exemplified by means of an example from structural mechanics.