Numerical methods for probalistic dimensioning and safety calculation

The computation of failure probability is substituted by the search for the minimum of a function, i.e. the smallest distance of the boundary state function to the origin of the coordinate system, in that case that the variables can be normalized and standardized in a convenient way. The corresponding solution algorithms are based on a piece wise iterative linearization of the boundary state function. It appears that there can be determined at least boundaries for the true failure probability. This contribution compiles the mathematical foundations and numerical problems of some of the techniques contained in the solution of the algorithm. Programmes are given in the appendix, that are written in ALGOL and have been tested (BETAABIT, BROYDEN, THETAIT). Any dimensioning problems, whose variables posess any distribution functions, can be solved. (orig./HP)