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Interaction Models as Alternatives to Low-Order Polynomials

Summary: One of the most popular classes of models that people fit empirically to data is the class of polynomials. One reason for this is, over limited-sized regions of interest, lower-degree polynomials (specifically, degrees 1, 2, and at most 3) have stood the test of time by proving their versatility when it comes to fitting a wide variety of different surface shapes. However, when faced with modeling a surface over an experimental region whose boundaries extend beyond some localized neighborhood or limited-sized region of interest, a polynomial of degree 2, or even of degree 3, may not be adequate. For this situation we propose fitting an interaction model which is a reduced form of a higher-degree polynomial. Several examples of actual experiments are presented to illustrate the improvement in fit by an interaction model over that of a standard polynomial, even for response surfaces with uncomplicated shapes.

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  • Topics: Design of Experiments
  • Keywords: Factorial designs,Interactions,Goodness of fit,Misspecification,Polynomial model,Response surface methodology (RSM)
  • Author: Cornell, John A.; Montgomery, Douglas C.
  • Journal: Journal of Quality Technology