A minimum aberration-type criterion for selecting space-filling designs

Abstract

Summary Space-filling designs are widely used in computer experiments. Inspired by the stratified orthogonality of strong orthogonal arrays, we propose a criterion of minimum aberration-type for assessing the space-filling properties of designs based on design stratification properties on various grids. A space-filling hierarchy principle is proposed as a basic assumption of the criterion. The new criterion provides a systematic way of classifying and ranking space-filling designs, including various types of strong orthogonal arrays and Latin hypercube designs. Theoretical results and examples are presented to show that strong orthogonal arrays of maximum strength are favourable under the proposed criterion. For strong orthogonal arrays of the same strength, the space-filling criterion can further rank them based on their space-filling patterns.