Approximation to multivariate normal integral and its application in time-dependent reliability analysis

摘要: Abstract It is common to evaluate high-dimensional normal probabilities in many uncertainty-related applications such as system and time-dependent reliability analysis. An accurate method proposed probabilities, especially when they reside tail areas. The probability at first converted into the cumulative distribution function of extreme value involved variables. Then series expansion employed approximate with respect a smaller number mutually independent standard moment generating obtained using Gauss-Hermite quadrature method. saddlepoint approximation finally used estimate value, thereby desired probability. then applied analysis where large dependent variables are use First Order Reliability Method. Examples show that generally more robust than widely randomized quasi Monte Carlo equivalent component