Fractional factorial designs with response surface models

At the outset of an experimental study, the shape of the response surface is not known. A quadratic model will be necessary only if the response surface is curved. It was discussed in Chapters 5 and 6 how linear and second-order interaction models can be established from factorial and fractional factorial designs, and how such models might be useful in screening experiments. However, these models cannot describe the curvatures of the surface, and should there be indications of curvature, it would be convenient if a complementary set of experiments could be run by which an interaction model could be augmented with squared terms. 

Steven Gilmour is Professor of Statistics in the School of Mathematical Sciences at Queen Mary, University of London. His interests are in the design and analysis of experiments with complex treatment structures, including supersaturated designs, fractional factorial designs, response surface methodology, nonlinear models, and random treatment effects. 

Let us now have a look at general screening experiments with many variables. Assume that k variables (xj, X2,..., xJ have been studied by a fractional factorial design and that a response surface model with linear and cross-product interaction terms has been determined. 

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