Uniform Designs On General Domains And Their Constructions

As one of important experimental designs, uniform design has been widely ap-plied in many fields, such as manufacturing, system engineering, pharmaceutics andnatural sciences since it appeared in late 1970's. Related theories on uniform uniformhave also been developed. However, up to now, most of these theories are restrictedto the analysis and construction of uniform designs on unit cube. Little attention hasbeen paid to uniform design on general domains.In this paper, a new measure of uniformity, i.e,λ-discrepancy, is defined for com-paring designs on arbitrary domains. Based on it, an optimization algorithm is pro-posed to construct related uniform designs. Take two dimensional Flexible regionswith several special parameters as examples, we compose some Matlab code and con-struct a number of uniform designs underλ-discrepancy. By comparing with thoseconstructed by using inverse transformation method and central composite discrep-ancy method, we find these newly obtained designs seem more symmetric and moreuniform and also have less mean square error, which shows the rationality and validityofλ-discrepancy.