Response Surface Designs for Estimating the Optimal Point

Abstract

The problem considered is that of choosing a k-factor design meant for locating the maximal (or minimal) point of a second order response surface. Using least squares estimates the deficiency of a design is defined as the expected difference between the optimum response and the true response at the estimated optimal point. It is first shown that a design which minimizes this deficiency must belong to a special subclass of designs. Each member of this subclass cam be represented by a distribution over the unit simplex in the k-dimensional positive orthant apportioning the whole mass exclusively between the origin and the outer surface. Using this result the global solution in some special cases and a restricted solution in the general case are obtained.