Exclusive Content & Downloads from ASQ

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.

Anyone with a subscription, including Site and Enterprise members, can access this article.

Other Ways to Access content:

Join ASQ

Join ASQ as a Full member. Enjoy all the ASQ member benefits including access to many online articles.

Subscribe to Journal of Quality Technology

Access this and ALL OTHER Journal of Quality Technology online articles. You'll also receive the print version by mail.

  • 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