Abstract
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.
Original language | English (US) |
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Pages (from-to) | 163-176 |
Number of pages | 14 |
Journal | Journal of Quality Technology |
Volume | 28 |
Issue number | 2 |
DOIs | |
State | Published - Apr 1996 |
Keywords
- Factorial Design
- Interactions
- Lack of Fit
- Misspecified Model
- Polynomial Model
- Response Surface Methodology
ASJC Scopus subject areas
- Safety, Risk, Reliability and Quality
- Strategy and Management
- Management Science and Operations Research
- Industrial and Manufacturing Engineering