An effective approximation to evaluate multinormal integrals

In structural system reliability theory, the evaluation of multivariate normal distributions is an important problem. Numerical integration of multinormal distributions with high accuracy and efficiency is known to be impractical when the number of distribution dimensions is large, typically greater than five. The paper presents a practical and effective approach to approximate a multinormal integral by a product of one-dimensional normal integrals, which are easy to evaluate. Examples considered in the paper illustrate a remarkable accuracy of the approximation in comparison with exact integration. Unlike a first-order multinormal approximation widely used in the literature, this method does not involve any iterative linearization, minimization or integration. Computational simplicity with high accuracy is the major advantage of the proposed method, which also highlights its potential for estimating reliability of structural systems. (C) 1998 Elsevier Science Ltd. All rights reserved.