New Algorithm for Structural Reliability Estimation

An efficient and accurate method for computing probabilities of failure, $p_f\text{,}$ of structural and mechanical components is presented. Limit state equations can be of any continuous functional form, and the basic variables can have any distribution. The algorithm that is an extension of the Rackwitz‐Fiessler and Chen‐Lind methods has the following qualities: (1) It employs an optimization routine to approxirhate nonnormal variants as equivalent normals; (2) approximates the limit state by a quadratic at the design point; and (3) transforms the quadratic form to a linear one, thereby approximating the limit state as linear in normal design factors. Exhaustive testing of the algorithm has indicated not only that computational time is “negligible,” but also that errors in $p_f$ are consistently less than 10% in all realistic physical problems and are usually much less. Examples are presented to illustrate the performance of this fast probability integration method.