Quadric reliability indices

Limit state models based on multi-dimensional rotational paraboloids and hyperboloids are described, and approximate closed form solutions obtained for the associated failure probability and corresponding reliability index. The solutions presented depend only on the number of variables, minimum distance of the limit state surface from the origin and mean curvature at the design point, in a standard normal space. These results extend the range of analytic solutions for reliability indices, from linear and spherical surfaces, to include these rotational quadrics, and so permit a wider choice of limit state models.