Practical First-Order Reliability Computations Using Spreadsheet

B. K. Low
School of Civil and Structural Engineering, Nanyang Technological University, Singapore

K. K. Phoon
Department of Civil Engineering, National University of Singapore, Singapore

The Hasofer-Lind (1974) index and the first order reliability method (FORM) have been treated in Rackwitz and Fiessler (1978), Ditlevsen (1981), Shinozuka (1983), Ang and Tang (1984), Madsen et al. (1986), and Tichy (1993). The continuing interest in FORM is also evident in Melchers (1999), Haldar and Mahadevan (1999), Nowak and Collins (2000), for example. The potential inadequacies of FORM in some special cases have been recognized, and more refined alternatives proposed (e.g. Der Kiureghian et al.1987). On the other hand, Rackwitz (2001) noted the usefulness and accuracy of FORM in most applications; some counterexamples were summarized, their rather extreme nature and artificiality noted, but their healthy role also admitted.

With respect to Hasofer-Lind index and FORM, a practical procedure was presented in Low and Tang (1997a). The Rackwitz-Fiessler equivalent normal transformation was used. The concepts of coordinate transformation and frame-of-reference rotation were not required. Correlation was accounted for by setting up the quadratic form directly. Iterative searching and partial derivatives were automatic using constrained optimization in the ubiquitous spreadsheet platform. 

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