The return of the design points

In the last decades simulation methods for calculating failure probabilities in structural reliability have become increasingly popular. The FORM/SORM concepts were discarded based on the claim that these methods do not work well for high dimensional problems and for multiple design points. From this it was concluded that design points are quite useless. This is based a confusion between the design point concept and the FORM/SORM approximation method. The Lemma of Hohenbichler shows that for small probabilities the probability content of the failure domain is concentrated around the design points, so these points are important. Their positions give further the conditional means of the points in the failure domains. Then it is proven that most of the alternative estimation methods, surrogate models, cross entropy, subset simulation and line sampling use implicitly design point concepts. All these approaches end up with a point clouds around the design points. Finally design point based methods are derived which are efficient for high dimensions and multiple design points.