The point-estimate method with large numbers of variables

Rosenbleuth's point-estimate method has become widely used in geotechnical practice for reliability calculations. Although the point-estimate method is a powerful and simple method for evaluating the moments of functions of random variables, it is limited by the need to make 2(n) evaluations when there are n random variables. Modifications of the method reduce this to 2(n) evaluations by using points on the diameters of a hypersphere instead of at the corners of the inscribed hypercube. However, these techniques force the co-ordinates of the evaluation points farther from the means of the variables; for a bounded variable, the points may easily fall outside the domain of definition of the variable. The problem can be avoided by using other techniques for some special cases or by reducing the number of random variables that must be considered. Copyright (C) 2002 John Wiley Sons, Ltd.