Reliability approximations via asymptotic distribution

ABSTRACT: In the reliability analysis of safety critical complex engineering structures a very large number of the system parameters can be considered to be random variables. The difficulty in computing the failure prob-ability using the classical First and Second-Order Reliability Methods (FORM and SORM) increases rapidly with the number of variables or ‘dimension’. There are mainly two reasons behind this. The first is the increase in computational time with the increase in the number of random variables. In principle this problem can be handled with superior computational tools. The second, which is perhaps more fundamental, is that there are some conceptual difficulties associated typically with high dimensions. This means that even one manages to carry out the necessary computations, the application of existing FORM and SORM may still lead to incorrect results in high dimensions. This paper is aimed at addressing this issue. Based on the asymptotic distribution of quadratic form in Gaussian random variables, two formulations for the case when the number of random variables n → ∞ is provided. The first is called strict asymptotic formulation and the second is called weak asymptotic formulation. Both approximations results in simple closed-form expressions for the probability of failure of an engineering structure. The proposed asymptotic approximations are compared with existing approximations and Monte Carlo simulations using numerical examples.