Interaction models as alternatives to low-order polynomials

被引:16
作者
Cornell, JA [1 ]
Montgomery, DC [1 ]
机构
[1] ARIZONA STATE UNIV,DEPT IND & MANAGEMENT SYST ENGN,TEMPE,AZ 85287
关键词
factorial design; interactions; lack of fit; misspecified model; polynomial model; response surface methodology;
D O I
10.1080/00224065.1996.11979657
中图分类号
T [工业技术];
学科分类号
08 ;
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.
引用
收藏
页码:163 / 176
页数:14
相关论文
共 7 条
[1]  
Box G. E. P., 1987, Empirical model-building and response surfaces
[2]   FITTING MODELS TO DATA FROM MIXTURE EXPERIMENTS CONTAINING OTHER FACTORS [J].
CORNELL, JA .
JOURNAL OF QUALITY TECHNOLOGY, 1995, 27 (01) :13-33
[3]  
DRAPER NR, 1981, APPLIED REGRESSION A
[4]  
Hoerl R., 1995, QUALITY MANAGEMENT J, V2, P58
[5]  
Khui A., 1987, RESPONSE SURFACES DE
[6]  
Myers R. H., 1995, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, DOI DOI 10.2307/1270613
[7]  
*SAS I INC, 1982, SAS US GUID STAT