Reliability indices employing measures of curvature

Abstract

A measure of average curvature of an n- variate failure surface is considered and shown to be of use in defining a comparable reliability index, as a combination of the curvature measure with a location parameter (Hasofer-Lind index). The form of this combination is derived by consideration of the probability content of offset hyperspheres in the space of the design variables. The resulting reliability index displays comparability (i.e. varies with the shape and location of the failure surface) whilst requiring much less computational effort than generalised indices based on the integration of density functions over the failure region or its complement. It also provides a means of defining an equivalent linear limit state surface.