Interaction Models as Alternatives to Low-Order Polynomials
作者:
CornellJohn A.,
MontgomeryDouglas C.,
期刊:
Journal of Quality Technology
(Taylor Available online 1996)
卷期:
Volume 28,
issue 2
页码: 163-176
ISSN:0022-4065
年代: 1996
DOI:10.1080/00224065.1996.11979657
出版商: Taylor&Francis
关键词: Factorial Design;Interactions;Lack of Fit;Misspecified Model;Polynomial Model;Response Surface Methodology
数据来源: Taylor
摘要:
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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