Efficient Spreadsheet Algorithm for First-Order Reliability Method

Abstract

A new spreadsheet-cell-object-oriented algorithm for the first-order reliability method is proposed and illustrated for cases with correlated nonnormals and explicit and implicit performance functions. The new approach differs from the writers earlier algorithm by obviating the need for computations of equivalent normal means and equivalent normal standard deviations. It obtains the solution faster and is more efficient, robust, and succinct. Other advantages include ease of initialization prior to constrained optimization, ease of randomization of initial values for checking robustness, and fewer required optimization constraints during spreadsheet-automated search for the design point. Two cases with implicit performance functions, namely an asymmetrically loaded beam on Winkler medium and a strut with complex supports are analyzed using the new approach and discussed. Comparisons are also made between the proposed approach and that based on Rosenblatt transformation.