Skip Navigation


Biometrika Advance Access originally published online on October 3, 2009
Biometrika 2009 96(4):945-956; doi:10.1093/biomet/asp044
This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Qian, P. Z. G.
Right arrow Articles by Wu, C. F. J.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2009 Biometrika Trust

Article

Sliced space-filling designs

Peter Z. G. Qian

Department of Statistics, University of Wisconsin-Madison, Wisconsin 53706, U.S.A. peterq{at}stat.wisc.edu

C. F. Jeff Wu

H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, U.S.A. jeffwu{at}isye.gatech.edu

Received for publication 1 June 2008. Revision received 1 March 2009.

We propose an approach to constructing a new type of design, a sliced space-filling design, intended for computer experiments with qualitative and quantitative factors. The approach starts with constructing a Latin hypercube design based on a special orthogonal array for the quantitative factors and then partitions the design into groups corresponding to different level combinations of the qualitative factors. The points in each group have good space-filling properties. Some illustrative examples are given.

Key Words: Bush’s construction • Computer experiment • Design of experiment • Difference matrix • Rao–Hamming construction



References

    Box G. E. P., Draper N. R. Empirical Model Building and Response Surfaces (1987) New York: Wiley.

    Draper N. R., John J. A. Response-surface designs for quantitative and qualitative factors. Technometrics (1988) 30:423–8.[CrossRef][Web of Science]

    Fang K. F., Li R. Z., Sudjianto A. Design and Modeling for Computer Experiments (2005) New York: Chapman & Hall/CRC Press.

    Han G., Santner T. J., Notz W. I., Bartel D. L. Prediction for computer experiments having quantitative and qualitative input variables. Technometrics (2009) 51:278–88.[CrossRef][Web of Science]

    Hedayat A., Sloane N. J. A., Stufken J. Orthogonal Arrays: Theory and Applications (1999) New York: Springer.

    Koehler J., Owen A. B. Computer experiments. In: Handbook of Statistics, 13: Design and Analysis of Experiments—Ghosh S., Rao C., eds. (1996) Amsterdam: North-Holland. 261–308.

    Lidl R., Niederreiter H. Finite Fields (Encyclopedia of Mathematics and Its Applications) (1997) 2nd ed. Cambridge: Cambridge University Press.

    McKay M. D., Conover W. J., Beckman R. J. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics (1979) 21:239–45.[CrossRef][Web of Science]

    McMillan N., Sacks J., Welch W., Gao F. Analysis of protein activity data by Gaussian stochastic process models. J. Biopharm. Statist. (1999) 91:145–60.

    Owen A. B. Orthogonal arrays for computer experiments, integration and visualization. Statist. Sinica (1992) 2:439–52.

    Qian P. Z. G., Tang B., Wu C. F. J. Nested space-filling designs for computer experiments with two levels of accuracy. Statist. Sinica (2009) 19:287–300.

    Qian P. Z. G., Wu H., Wu C. F. J. Gaussian process models for computer experiments with qualitative and quantitative factors. Technometrics (2008) 50:383–96.[CrossRef][Web of Science]

    Santner T. J., Williams B. J., Notz W. I. The Design and Analysis of Computer Experiments (2003) New York: Springer.

    Schmidt R. R., Cruz E. E., Iyengar M. K. Challenges of data center thermal management. IBM J. Res. Develop. (2005) 49:709–23.

    Tang B. Orthogonal array-based Latin hypercubes. J. Am. Statist. Assoc. (1993) 88:1392–7.[CrossRef][Web of Science]

    Wu C. F. J., Ding Y. Construction of response surface designs for qualitative and quantitative factors. J. Statist. Plan. Infer. (1998) 71:331–48.[CrossRef]


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?



This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Qian, P. Z. G.
Right arrow Articles by Wu, C. F. J.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?