The Exploration and Exploitation of Response Surfaces: Some General Considerations and Examples

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Abstract
When a measured response depends functionally on a group of k quantitative variables or factors, the response function can be represented as a surface in a (k + l)-dimensional space. Although such models may be applied to many different fields, they are particularly useful in chemical expts. in which an optimum response such as maximum yield is sought. The author discusses methods for exploring such response surfaces and proposes new techniques which are much superior to the conventional "one factor at a time" procedure. In connection with factor dependence, a sharp distinction is made between "natural" variables, such as temperature or concentration, and fundamental variables such as the frequency of a particular type of molecular collision. Response surfaces frequently have no unique maximum when measured in terms of "natural" variables, and the proposed methods not only allow the experimenter to characterize the surface accurately but they may also lead him to a more fundamental understanding of the basic process mechanisms. The technique consists of a sequential approach to the neighborhood of a maximum with a series of small expts. and the use of the method of steepest ascent. At this point a second or third degree equation is fitted by the method of least squares and the fitted surface is examined carefully. The author discusses the general principles associated with his method and cites three examples which present interesting response surfaces. Detailed calculations are given elsewhere in the literature.

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