Point-Estimate Method as Numerical Quadrature

Abstract

Rosenblueth's point-estimate method for approximating the low-order moments of functions of random variables is widely used in geotechnical reliability analyses. It is a special case of numerical quadrature based on orthogonal polynomials. For normal variables, it corresponds to Gauss-Hermite quadrature, but Rosenblueth's procedure automatically generates the weights and abscissas of Gauss-Legendre and Gauss-Laguerre quadrature as well. Despite beliefs to the contrary, the method is not a form of Monte Carlo simulation or FOSM Taylor series expansion. The method is reasonably robust and can be satisfactorily accurate for a wide range of practical problems, although the computational requirements increase rapidly with the number of uncertain quantities. Caution should be exercised in applying the method when transformation of the uncertain quantities severely changes the form of the distributions or when moments of order greater than the two are involved. Examples with closed-form solutions serve to illustrate the use and accuracy of the method.