System reliability analysis for mixed uncertain variables

Uncertainties in a physical system should be modeled accurately to obtain an accurate estimate of its safety. Based on the amount and type of information available, either probability theory or possibility theory can be used. In probability theory variation in the parameters is modeled using probability density functions and in possibility theory it is modeled using fuzzy membership functions. But when dealing with a combination of both probability distributions and fuzzy membership functions, the computational cost involved in estimating the bounds of reliability increases exponentially because one reliability analysis, which is a computationally expensive procedure, is performed at each possibility level. Moreover, the failure of structural systems is governed by multiple limit-state functions, all of which are to be taken into consideration for determining its safety. These limit-state functions are often correlated and the accuracy of the estimated system reliability is dependent on the ability to model the joint failure surface. To reduce the computational cost involved without loss of accuracy, high quality function approximations for each of the limit-states and the joint failure surface are developed in this paper. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed methodology.