Improved approximation for multinormal integral

Improvements on the approximate solutions for the standard multinormal or multivariate normal distribution function based on the first order structural reliability concepts are proposed. The numerical accuracy and efficiency of three methods of obtaining the solutions are compared. For parallel systems problems, it is shown that the suggested first order multinormal (FOMN) approach produces results significantly closer to the exact answer than either those of the crude or the improved FOMN solutions. The performance of the improved and general FOMN approaches when applied to high reliability series systems appears to be as good as or even better than those obtained by the well-known second order bounds.