Asymptotic Approximation of Probability Integrals with Applications to Reliability of Uncertain Dynamical Systems

New asymptotic approximations of reliability integrals are developed in both the spaces of original and transformed (independently, normally distributed) variables. In the transformed variables, the approximation yields a very simple formula for approximating the value of SORM integrals. Examples are presented illustrating the accuracy of the approximations and results are compared with some existing approximations of reliability integrals.