Flexible Response Surface Methods via Spatial Regression and Eblups

Abstract

Spatial regression models provide a complementary alterna-tive to polynomial response surface methods in the context of process opti-mization. The models enable estimation of design variable effects and, via EBLUPS, smooth data-faithful approximations to the unknown response function over the design space. The covariance structure of the particular spatial models drives the predicted response surfaces and both isotropic and geometrically anisotropic forms are considered. Estimation of covari-ance parameters is achieved via maximum likelihood or restricted maxi-mum likelihood. A feature of the method is the visually appealing graphical summaries that are produced. These allow rapid identification of process windows on the design space for which the response(s) achieves target per-formance. The models perform well in association with spatial designs such as the maximin and minimax designs. The EVOP approach is also possible and in this context the models provide a representation of the response over the entire series of designs. An example involving the optimization of assay components in a DNA amplification procedure provides illustration.