On the approximations for multinormal integration

The system failure probability in structural reliability analysis involves the computation of multivariate normal integrals. The civil and structural engineering literature has seen the development of several approximation methods for the computation of multivariate normal integrals. However, these developments have been totally unaware of the same in the statistics literature. In this note, a 1-line program from a freely downloadable statistical software is provided for the exact computation of m-dimensional multinormal integrals. It is shown that at least two of the known methods from the civil and structural engineering literature lead to inaccurate results.