Graphical Assessment of the Prediction Capability of Response Surface Designs

Ann Giovannitti-Jensen · Raymond H. Myers

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Optimal Experimental Design Methods Advanced Statistical Methods and Models Gaussian Processes and Bayesian Inference

Abstract

Measures of the quality of prediction at locations on the surface of a hyperspherc are presented. These measures are used to form a graphical method of assessing the overall prediction capability of an experimental design throughout the region of interest. A plot of the spherical variance and the maximum and minimum prediction variances for locations on a sphere against the radius of the sphere. a vuriance dispersion graph. is used to give a comprehensive picture of the behavior of the prediction variances throughout a region and hence of the quality of the predicted responses obtained with a particular design. Such plots are used to investigate and compare the prediction capabilities of certain response surface designs currently available to the researcher.

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References

1988Empirical Model Building and Response Surfaces 1960Some New Three Level Designs for the Study of Quantitative Variables 1996Response Surface Methodology 1992On the Experimental Attainment of Optimum Conditions 1957Multi-Factor Experimental Designs for Exploring Response Surfaces 1959A Basis for the Selection of a Response Surface Design 1992Optimum Experimental Designs 1954The Exploration and Exploitation of Response Surfaces: Some General Considerations and Examples

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1993A new approach to the construction of optimal designs 2016I-Optimal Design of Mixture Experiments 2002Evaluation of Statistical Designs for Experiments Involving Noise Variables 1992Variance Dispersion Properties of Second-Order Response Surface Designs 1995Spherical Prediction-Variance Properties of Central Composite and Box-Behnken Designs 2000A Class of Three-Level Experimental Designs for Response Surface Modeling

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