Integration formulas to evaluate functions of random variables

Structural reliability analysis often involves extensive integration of a function of multiple basic variables. Special techniques can be used to reduce this numerical effort. This paper develops integration formulas for computing the statistical parameters of a function of a random vector, in particular calculation of the first few moments. The formula is a numerical procedure using selected weights and points to estimate integrals. The points and weights are predetermined in the independent standard normal variable space. The sample points in basic variable space are then obtained by various transformations. The formulas were developed for the basic variables with various probability information known. The procedure is convenient to implement, and allows for a direct use of the available deterministic computer programs.