Title: Measures of uniformity for space-filling uniform designs in a spherical region

Authors: Ismael S. Talke; John J. Borkowski

Addresses: Department of Information Systems and Analytics, Miami University, Oxford, OH 45056, USA ' Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717, USA

Abstract: The focus of this paper is to present and discuss new discrepancy measures of uniform designs (UDs) in the two- and three-dimensional spherical design regions B² and B³. The good lattice point (glp) method is used to construct the UDs in B² and B³ because it generates good space-filling designs with low discrepancy and designs having small distance-based measures of uniformity. The best UDs were found in B² and B³ for newly proposed discrepancy criteria. Best UDs based on three distance-based assessment criteria are also included for comparison. Distance-based criteria are alternative measures for design generation in higher-dimensional spherical regions with an example of design generation presented for B⁴.

Keywords: discrepancy; distance-based criteria; experimental design; glp; good lattice point; spherical design regions; uniformity measures; space-filling uniform designs.

DOI: 10.1504/IJEDPO.2016.080509

International Journal of Experimental Design and Process Optimisation, 2016 Vol.5 No.1/2, pp.23 - 40

Received: 04 Sep 2015
Accepted: 31 Jan 2016
Published online: 28 Nov 2016 *

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