Response surface methodology

In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. The method was introduced by G. E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an optimal response. Box and Wilson suggest using a second-degree polynomial model to do this. They acknowledge that this model is only an approximation, but use it because such a model is easy to estimate and apply, even when little is known about the process.

Statistical approaches such as RSM can be employed to maximize the production of a special substance by optimization of operational factors. In contrast to conventional methods, the interaction among process variables can be determined by statistical techniques.

An easy way to estimate a first-degree polynomial model is to use a factorial experiment or a fractional factorial design. This is sufficient to determine which explanatory variables affect the response variable(s) of interest. Once it is suspected that only significant explanatory variables are left, then a more complicated design, such as a central composite design can be implemented to estimate a second-degree polynomial model, which is still only an approximation at best. However, the second-degree model can be used to optimize (maximize, minimize, or attain a specific target for).

(RESPONSE SURFACE OPTIMIZATION USING JMP SOFTWARE)

ORTHOGONALITY: The property that allows individual effects of the k-factors to be estimated independently without (or with minimal) confounding. Also orthogonality provides minimum variance estimates of the model coefficient so that they are uncorrelated.

ROTATABILITY: The property of rotating points of the design about the center of the factor space. The moments of the distribution of the design points are constant.

UNIFORMITY: A third property of CCD designs used to control the number of center points is uniform precision (or Uniformity).

Cubic designs are discussed by Kiefer, by Atkinson, Donev, and Tobias and by Hardin and Sloane.

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