# Principle of Normal Tail Approximation

*by*Ove Ditlevsen, Prof. of Applied Mathematics in Civ. Engrg.; Danish Engrg. Academy, Building 373, DK 2800, Lyngby, Denmark,

**Serial Information**:

*Journal of the Engineering Mechanics Division*, 1981, Vol. 107, Issue 6, Pg. 1191-1208

**Document Type:**Journal Paper

**Abstract:**

A difficult problem in general multivariable structural reliability problems of limit state type is to calculate the probability content of the failure set. Very often, however, practical problems have such nice properties that the failure probability may be assessed in a sample way and with sufficient accuracy solely by use of hyperplane approximations to the failure surface as represented in a space in which the basic random variables appear as transformed into mutually independent standardized normal random variables. The approximation points are those origin projection points which are local minimum points for the distance from the origin to the failure surface points. It is proven that these critical points may be determined by iterative use of the principle of normal tail approximation. For hyperplane failure surfaces in the original space of basic variables this method preserves the advantage of second moment reliability calculus. The method is illustrated on an example of its own value. It concerns the determination of the predictive distribution of a material strength quantity, say, given no direct observations. Data are solely indirect such as they result typically in non-destructive testing.

**Subject Headings:**Failure analysis | Approximation methods | Structural reliability | Probability | Surface properties | Strength of materials | Limit states | Structural failures

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