On Uniform Design of Experiments With Restricted

In this paper we propose a new method, based on the conditional distribution method in Monte-Carlo methods, to generate the uniform distribution on the domain T n (a; b) = f(x 1 ; ; x n) : 0 a i x i b i 1; 0 i n; x 1 + + x n = 1g, where a = (a 1 ; ; a n) and b = (b 1 ; ; b n). By this new method we can easily obtain uniform designs of experiments with mixtures, i.e., to generate a set of points that are uniformly scattered on the domain T n (a; b). This approach can apply to generation of uniform distributions on various domains, such as convex polyhedron, simplex. These uniform distributions are useful in experimental design, reliability and optimization.