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Abstract
Often, second-order response surface designs are chosen on the basis of a single-valued criterion such as D- or G-optimality. While such criteria provide a useful basis for selecting designs, they often fail to convey the true nature of the design's support of the fitted model in terms of prediction properties over a region of interest. As an alternative to a single-valued criterion, we propose variance dispersion graphs to compare various second-order response surface designs. This graphical procedure is used to examine the relative strengths and weaknesses of such popular designs as the central composite, Box-Behnken, and small composite. Areas in the region of interest where prediction is relatively good and relatively poor are discussed, and designs which have good overall performance are highlighted. A summary comparison of such saturates or near-saturates designs as the hybrid, Box-Draper, and Notz designs is given together with recommendations concerning the proper choice among these designs. Finally, we show how the use of the D-optimality criterion can lead to misleading results when the user is truly interested in response surface prediction.
Additional information
Notes on contributors
Raymond H. Myers
Dr. R. Myers is a Professor in the Department of Statistics.
G. Geoffrey Vining
Dr. Vining is an Assistant Professor in the Department of Statistics. He is a Senior Member of ASQC.
Ann Giovannitti-Jensen
Dr. Giovannitti-Jensen is a Senior R&D Statistician.
Sharon L. Myers
Dr. S. Myers is an Assistant Professor in the Department of Statistics.
