A CONSTRUCTION METHOD FOR ORTHOGONAL LATIN HYPERCUBE DESIGNS WITH PRIME POWER LEVELS

Fang Pang · Min‐Qian Liu · Dennis K. J. Lin

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Optimal Experimental Design Methods Advanced Combinatorial Mathematics Mathematical Approximation and Integration

Abstract

Latin hypercube design (LHD) is popularly used in designing computer experiments. This paper explores how to construct LHDs with p d (d = 2 c ) runs and up to (p d − 1)/(p − 1) factors in which all main effects are orthogonal. This is accomplished by rotating groups of factors in a p d -run regular saturated factorial design. These rotated factorial designs are easy to construct and preserve many attractive properties of standard factorial designs. The proposed method covers the one by Steinberg and Lin (2006) as a special case and is able to generate more orthogonal LHDs with attractive properties. Theoretical properties as well as the construction algorithm are discussed, with an example for illustration.

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References

2000A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code 1993Orthogonal Array-Based Latin Hypercubes 1959A Basis for the Selection of a Response Surface Design 1998Orthogonal Column Latin Hypercubes and Their Application in Computer Experiments 2008ORTHOGONAL-MAXIMIN LATIN HYPERCUBE DESIGNS 2006A construction method for orthogonal Latin hypercube designs 2001Optimal and orthogonal Latin hypercube designs for computer experiments 1998SELECTING LATIN HYPERCUBES USING CORRELATION CRITERIA

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2011Construction of orthogonal and nearly orthogonal latin hypercube designs from orthogonal designs 2010Construction of orthogonal Latin hypercube designs with flexible run sizes 2014Design for computer experiments with qualitative and quantitative factors 2012Constructing nearly orthogonal latin hypercubes for any nonsaturated run-variable combination 2016A Method of Constructing Space-Filling Orthogonal Designs

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