Third moment method for reliability analysis involving independent parametric probability-boxes

Reliability analysis aims to evaluate the failure probability of a structure or structural system under the presence of aleatory uncertainties. However, in practical cases, aleatory uncertainties may be accompanied by uncertainties of the epistemic type, leading to a so-called hybrid problem. These hybrid uncertainties can be modeled in certain cases using probability distributions with parameters characterized as intervals, leading to so-called parametric probability-boxes. In this study, a third moment method is proposed for reliability analysis involving independent parametric probability-boxes. Uncertainties in the first three moments of random variables are considered and modeled by intervals. With the aid of third moment normal transformation techniques, the values of uncertain moments of each parametric probability-box that lead to the bounds of failure probability are determined. Then, the bounds of failure probability can be evaluated by performing two reliability analyses. The application of the proposed method is illustrated by both numerical and practical examples, including nonlinear and finite element problems.