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Computer models play an increasingly important role in engineering design and in the study of complex systems, where physical experiments on the real system or even a prototype are prohibitively expensive. Both deterministic and stochastic computer models are used in these situations. A deterministic computer model is a set of complex equations whose solution depends on the input conditions and the levels of design factors or parameters but not on random elements. Examples include finite element models and computational fluid dynamics models. Space-filling designs are usually employed to study these deterministic computer models and often the modeling strategy involves fitting a spatial correlation or Kriging model (the Gaussian stochastic process model) to the data, because this model interpolates the experimental data exactly. We provide a survey of these designs and the modeling strategy, and propose a new type of hybrid space-filling design. The new design is a hybrid consisting of design points from a traditional space-filling design augmented by runs from a near saturated I-optimal design for a polynomial. We illustrate the construction of these designs with examples, and demonstrate their performance in response prediction for several situations. A comparison with standard space-filling designs is provided.
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Allen, T. T., Bernshteyn, M. A., & Kabiri-Bamoradian, K. (2003). Constructing meta-models for computer experiments. Journal of Quality Technology, 35(3), 264–274.
Ankenman, B., Nelson, B. L., & Staum, J. (2008). Stochastic kriging for simulation metamodeling. In Proceedings of the 2008 winter simulation conference, Miami (pp. 362–370).
Bursztyn, D., & Steinberg, D. M. (2006). Comparison of designs for computer experiments. Journal of Statistical Planning and Inference, 136, 1103–1119.
Chen V., Tsui, K-L., Barton, R., & Meckensheime, M. (2006). A review on design, modeling and applications of computer experiments. IEE Transactions, 38, 273–291.
Fang, K. T., Li, R., & Sudjianto, A. (2006). Design and modeling for computer experiments. Boca Raton: Taylor & Francis.
Hussain, M. F., Barton, R. R., & Joshi, S. B. (2002). Metamodeling: Radial basis functions, versus polynomials. European Journal of Operational Research, 138, 142–154.
Johnson, R. T., Montgomery, D. C., Jones, B., & Parker, P. A. (2010). Comparing computer experiments using high order polynomial metamodels. Journal of Quality Technology, 42(1), 86–102.
Johnson, R. T., Montgomery, D. C., & Jones, B. (2010). An empirical study of the prediction performance of space-filling designs. International Journal of Experimental Design and Process Optimisation (to appear).
Jones, B., & Johnson, R. T. (2009). The design and analysis of the gaussian process model. Quality and Reliability Engineering International, 25, 515–524.
Loeppky, J.L., Sacks, J., & Welch, W. (2008). Choosing the sample size of a computer experiment: A practical guide. Technical Report Number 170, National Institute of Statistical Sciences.
McKay, N. D., Conover, W. J., & Beckman, R. J. (1979). A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21, 239–245.
Montgomery, D. C. (2009). The design and analysis of experiments, 7th ed. New York: Wiley.
Morris, M. D., Mitchell, T. J., & Ylvisaker, D. (1993). Bayesian design and analysis of computer experiments: Use of derivatives in surface prediction. Technometrics, 35, 243–255.
Myers, R. H., Montgomery, D. C., & Anderson-Cook, C. M. (2002). Response surface methodology: process and product optimization using designed experiments, 3rd ed. New York: John.
Santner, T. J., Williams, B. J., & Notz, W. I. (2003). The design and analysis of computer experiments. Springer series in statistics. New York: Springer.
Storlie, C. B., & Helton, J. C. (2008). Multiple predictor smoothing methods for sensitivity analysis: Example results. Reliability Engineering & System Safety, 93, 55–77.
Welch, W. J., Buck, R. J., Sacks, J., Wynn, H. P., Mitchell, T. J., & Morris, M. D. (1992). Screening, predicting, and computer experiments. Technometrics, 34(1), 15–25.
Zahran, A., Anderson-Cook, C. M., & Myers, R. H. (2003). Fraction of design space to assess the prediction capability of response surface designs. Journal of Quality Technology, 35, 377–386.
- Hybrid Space-Filling Designs for Computer Experiments
Rachel T. Johnson
Douglas C. Montgomery
Kathryn S. Kennedy
- Physica-Verlag HD
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