Approximate solutions to the general structural reliability problem, i.e., computing probabilities of complicated functions of random variables, can be obtained efficiently by the fast probability integration (FPI) methods of Rackwitz-Fiessler and Wu. Relative to Monte Carlo, FPI methods have been found by the authors to require only about 1/10 of the computer time for probability levels of about 10−3. For lower probabilities, the differences are more dramatic. FPI can also be employed in situations, e.g., finite element analyses when the relationship between variables is defined only by a numerical algorithm. Unfortunately, FPI requires an explicit function. A strategy is presented herein in which a computer routine is run repeatedly k times with selected perturbed values of the variables to obtain k solutions for a response variable Y. An approximating polynomial is fit to the k “data” sets. FPI methods are then employed for this explicit form. Examples are presented of the FPI method applied to an explicit form and applied to a problem in which a polynomial approximation is made for the response variable of interest.

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