Multinormal probability by sequential conditioned importance sampling: theory and application

An efficient Monte Carlo simulation algorithm is developed for estimating the probability content of rectangular domains in the multinormal probability space. The algorithm makes use of the properties of the multinormal distribution, as well as the concept of importance sampling. Accurate estimates of the probability are obtained with a relatively small number of simulations, regardless of its magnitude. The algorithm also allows easy computation of the sensitivities of the probability with respect to distribution parameters or the boundaries of the domain. Application of the algorithm to structural system reliability is demonstrated through a simple example.