Efficient Reliability Evaluation Using Spreadsheet

A practical method using spreadsheets is proposed for calculating the Hasofer-Lind second moment reliability index β. Two example problems involving correlated normals and correlated nonnormals, respectively, are solved and compared with established mathematical approach. The proposed method is based on the perspective of an ellipsoid that is tangent to the failure surface in the original space of the random variables; concepts of transformed space or reduced variates are not required. Correlation is accounted for by setting up the quadratic form in the spreadsheet. Nonnormals are dealt with using established relationships between nonnormal distribution and its equivalent normal distribution. Iterative searching is performed automatically by invoking a spreadsheet's optimization tool. An advantage of the spreadsheet method is that partial derivatives are not part of the input; the method may therefore be especially attractive for cases with complicated or nonexplicit performance functions.