Orthogonal-column Latin hypercube designs with small samples

Latin hypercube designs with zero pair-wise column correlations are examined for their space-filling properties. Such designs, known as orthogonal-column Latin hypercube designs, are often used in computer experiments and in screening experiments, since all coefficients in a first-order model are estimated independently of each other. This makes interpretation of the factor effects particularly simple. Complete or partial enumeration searches are carried out to investigate the space-filling properties of all orthogonal-column Latin hypercube designs, with from 5 to 9 runs, and, from 2 to 5 factors. In cases where there are several designs with similar properties, the designs with minimum mean squared distance are determined. The maximum number of factors that can be accommodated in orthogonal-column Latin hypercube designs is determined for each design size, and designs found by various algorithmic methods proposed in the literature are identified.

[1]  W. Welch.  A mean squared error criterion for the design of experiments , 1983 .

[2]  V. R. Joseph,et al.  ORTHOGONAL-MAXIMIN LATIN HYPERCUBE DESIGNS , 2008 .

[3]  Boxin Tang,et al.  SELECTING LATIN HYPERCUBES USING CORRELATION CRITERIA , 1998 .

[4]  M. E. Johnson,et al.  Minimax and maximin distance designs , 1990 .

[5]  Dick den Hertog,et al.  Maximin Latin Hypercube Designs in Two Dimensions , 2007, Oper. Res..

[6]  Edwin R. van Dam,et al.  Bounds for Maximin Latin Hypercube Designs , 2007, Oper. Res..

[7]  Boxin Tang.  Orthogonal Array-Based Latin Hypercubes , 1993 .

[8]  K. Fang,et al.  Number-theoretic methods in statistics , 1993 .

[9]  Wim C. M. Van Beers.  Kriging metamodeling in discrete-event simulation: an overview , 2005, Winter Simulation Conference.

[10]  T. J. Mitchell,et al.  Exploratory designs for computational experiments , 1995 .

[11]  Dennis K. J. Lin,et al.  A construction method for orthogonal Latin hypercube designs , 2006 .

[12]  M. D. McKay,et al.  A comparison of three methods for selecting values of input variables in the analysis of output from a computer code , 2000 .

[13]  Kenny Q. Ye.  Orthogonal Column Latin Hypercubes and Their Application in Computer Experiments , 1998 .

[14]  Neil A. Butler,et al.  Optimal and orthogonal Latin hypercube designs for computer experiments , 2001 .

[15]  Kenny Q. Ye,et al.  Algorithmic construction of optimal symmetric Latin hypercube designs , 2000 .

[16]  T. M. Cioppa,et al.  Efficient Nearly Orthogonal and Space-Filling , 2007 .

[17]  Henry P. Wynn,et al.  Screening, predicting, and computer experiments , 1992 .

[18]  Boxin Tang.  A theorem for selecting OA-based Latin hypercubes using a distance criterion , 1994 .

[19]  Eva Riccomagno,et al.  Experimental Design and Observation for Large Systems , 1996, Journal of the Royal Statistical Society: Series B (Methodological).

[20]  Michael D. McKay,et al.  Latin hypercube sampling as a tool in uncertainty analysis of computer models , 1992, WSC '92.

[21]  Jeong‐Soo Park.  Optimal Latin-hypercube designs for computer experiments , 1994 .

[22]  Thomas W. Lucas,et al.  Efficient Nearly Orthogonal and Space-Filling Latin Hypercubes , 2007, Technometrics.

[23]  W.C.M. van Beers,et al.  Kriging Metamodeling for Simulation , 2005 .

[24]  H. D. Patterson.  The Errors of Lattice Sampling , 1954 .