A Generalization of the Response Surface Mean Square Error Criterion with a Specific Application to the Scope

Abstract

A response surface criterion for design selection is developed in this paper for the case of estimation of a set of parametric functions rather than a single response. A specific application is emphasized, that in which interest, centers on the partial derivat. ives of the response function. Both bias and variance of the parametric functions are taken into consideration. For the case of the slope of the response function two situations are given special emphasis; the fitting of a first order model in the presence of a true second order structure, and the fitting of a second order function in the presence of a third order alternative. The traditional response surface bias and variance criteria arise as a special case for the situation in which a single parametric function is merely the ordinary response surface.

KEY WORDS:

• Response Surface
• Slope
• Minimitm Bias
• Minimum Variance
• Design Moments
• Alternative Model
• Polynomial Model