Reliability analysis using object-oriented constrained optimization

A practical procedure is presented for reliability analysis involving correlated nonnormals. Equivalent normal transformation is performed as in the first order reliability method; the correlation matrix is used as it is without orthogonal transformation. Performance functions appear as simple spreadsheet cell objects but may embody substantial user-created program codes. The multidimensional equivalent dispersion ellipsoid is likewise a single cell object that contains various spreadsheet routines for equivalent normal transformation and matrix operations. The procedure can be viewed as the constrained optimization of the equivalent hyperellipsoid (yielding the reliability index) in the original space, and is automatic and efficient in the ubiquitous spreadsheet platform. Different probability distributions can be selected at ease and conveniently transformed to equivalent normals using a short program code given in the paper. Illustrations are presented using a three-variate simple performance function and various combinations of ten common distributions. This is followed by two relatively complicated examples, namely an asymmetrically loaded beam on Winkler medium, and a complex strut with implicit performance function. The probabilities of failure inferred from reliability indices are compared with Monte Carlo simulations. The simplicity, transparency and flexibilities of the object-oriented constrained optimization approach are demonstrated. (C) 2003 Elsevier Ltd. All rights reserved.