An efficient method for the estimation of structural reliability intervals with random sets, dependence modeling and uncertain inputs

• Random set theory is used for calculating the upper and lower bounds on the failure probability.
• The method allows the modelation of dependence between the input variables by means of copulas.
• The method reduces drastically the number of focal element evaluations.

A general method for estimating the bounds of the reliability of a system in which the input variables are described by random sets (probability distributions, probability boxes, or possibility distributions), with dependence modeling is proposed. The method is based on an analytical property of the so-called design point vector; this property is exploited by constructing a nonlinear projection of Monte Carlo samples of the input variables in a two-dimensional diagram from which the analyst can easily extract the relevant samples for computing both the lower and upper bounds of the failure probability using random set theory. The method, which is illustrated with some examples, represents a dramatic reduction in the number of focal element evaluations performed when applying the Monte Carlo method to random set theory.