Composite Response Surface Designs for Factors With Jointly Symmetric Effects

Abstract

In most applications of response surface analysis based on polynomial regression, complete first- or second-order linear models are used at least initially to represent the functional relationships between independent variables and expected responses. In some settings, however, knowledge of the physical system under study can (and should) be used to modify the model form. One such situation is found in mixture problems, where constraints on the independent proportions mathematically imply a reduction in the number of model terms for polynomials of any order. Another such situation is when some of the experimental factors have a kind of joint symmetric effect on the responses of interest. We describe a real experiment of this type, part of a research program focused on the design of a control system for an agricultural combine, and consider how the statistical model can be simplified and standard second-order composite designs can be modified to take advantage of this structure.