Experimental design for estimating the optimum point in a response surface

Abstract

The problem of optimal experimental design for response optimization is considered. The optimal point (control)x* of a response surface is to be determined by estimating the response parametersθ from measurements performed at design pointsxi,i=1,...,N. Classical sequential approaches for choosing thexi's are recalled. A loss function related to the issue of response optimization is used to define control-oriented design criteria. The design policies differ depending on whether least-squares or minimum risk estimation is used to estimateθ. Connections between various criteria suggested in the literature are exhibited. Special attention is given to quadratic model responses. Most approaches presented assume that the response is correctly described by a given parametric function over the region of interest. Possible deterministic departures from this function raise the problem of model robustness, and the literature on the subject is briefly surveyed.