Uniform Design in Computer and Physical Experiments

Abstract

Computer experiments have been widely used in various fields of industry, system engineering, and others because many physical phenomena are difficult or even impossible to study by conventional experimental methods. Design and modeling of computer experiments have become a hot topic since late Seventies of the Twentieth Century. Almost in the same time two different approaches are proposed for design of computer experiments: Latin hypercube sampling (LHS) and uniform design (UD). The former is a stochastic approach and the latter is a deterministic one. A uniform design is a low-discrepancy set in the sense of the discrepancy, the latter is a measure of uniformity. The uniform design can be used for computer experiments and also for physical experiments when the underlying model is unknown. In this paper we review some developments of the uniform design in the past years. More precisely, review and discuss relationships of fractional factorial designs including orthogonal arrays, supersaturated designs and uniform designs. Some basic knowledge of the uniform design with a demonstration example will be given.