## ABSTRACT

The underlying idea on the imprecise probability theory consists in modelling an imprecise probability distribution by a set of candidate probability distributions which are derived from the available data. The family is represented through a probability bounding approach applied to specify the lower and upper bounds of the imprecise probability distribution. A number of set-based uncertainty models derived from the probability bounding approach have been considered, namely the probability box structure. Designed from different approaches, probability boxes may differ meaningly from each other. A parametric approach may involve distributions with interval parameters or an envelope of competing probabilistic models. From search amid the number of candidate cumulative distribution functions the envelope of competing probabilistic models is expressed by a probability box function. In this way, a procedure for construction of a probability box structure by optimisation is advanced. Different dependencies may lead to quantitatively varied results so that a single scalar measure of a correlation coefficient may not be able to capture the complexity of the dependence model. Thus, the effects of correlation on the probability box structure may be comparatively considered. The technology is demonstrated on a synthetic exercise and on a design example referred to a strip spread foundation designed by the Eurocode 7.