The encounter of interval and probabilistic approaches to structural reliability at the design point

The consideration of uncertainties in structural analysis has traditionally been made in the field of structural reliability within the framework of classical probability theory. In many cases, however, there is no sufficient probabilistic information to substantiate such an approach. In recent years several non-probabilistic methods have been proposed as alternatives. One of them is the interval analysis, oriented to estimate the range of variation of output structural variables given the ranges of the input ones. The method, however, requires the use of special arithmetics which renders its application unpractical for structural analysis based on finite elements or other numerical techniques. In this paper a Monte Carlo method that can be applied to probabilistic as well as to interval approaches to reliability analysis is proposed. It is based on the optimal properties of the classical design point of probabilistic structural reliability. In particular, it is shown that the order statistics of the output variable is concealed in a plot defined by the design point vector. This facilitates the selection of the relevant samples for either interval or probability-based analysis. The examples show that the desired interval of the response or the failure probability can be accurately estimated on such a basis. The paper also discusses the use of Monte Carlo methods for both reliability and interval analysis from the point of view of the proposed representation.

► It is shown that the design point vector realizes the order statistics of output variables and the sample clustering.
► A standard plot in two dimensions showing the interval of the output variable is produced.
► The discrimination of safe and unsafe samples is also made visible.
► The use of interval arithmetics is overcome for interval estimation.