Uniform Designs Limit Aliasing

This paper shows how uniform designs can reduce this aliasing. The discrepancy is a quantitative measure of how uniformly design points are placed on an experimental domain. It is shown that in very general situations low-discrepancy designs limit aliasing. For the case of regular fractional factorial designs it is shown that minimum discrepancy designs have maximum resolution and minimum aberration. Since the concept of discrepancy is more general than resolution or aberration, discrepancy can be used to generalize the definitions of resolution and aberration to other types of designs. 1. Introduction. There are di#erent approaches to experimental design. If the form of the model relating the response to the factors is known, then optimal designs can be used to estimate the unknown parameters e#ciently. However, in many cases one does not know the form of the model a priori. Rather the model is selected based on regression diagnostics when analyzing the experimental data. Uniform designs (Wang and Fang, 1981, Fang and Wang, 1994, Bates et al., 1996) spread experimental points evenly over the domain. It is shown in this article that such an approach reduces the e#ect of aliasing, i.e., the extent to which terms not included in the model a#ect the estimates of terms included in the model. For fractional factorial designs, it is shown that uniform designs are equivalent to designs with minimum aberration. Suppose that an experiment has s factors and the design region i