Factorial Designs, the |X′X| Criterion, and Some Related Matters
作者:
M.J. Box,
N.R. Draper,
期刊:
Technometrics
(Taylor Available online 1971)
卷期:
Volume 13,
issue 4
页码: 731-742
ISSN:0040-1706
年代: 1971
DOI:10.1080/00401706.1971.10488845
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
Two of the basic approaches to choosing ann-point experimental design in many industrial situations are (i) to set down a simple factorial or fractional factorial design in the factors being studied, or (ii) to choose a design based on the well-known |X′X| criterion. Experimenters often prefer (i) due to its simplicity; our viewpoint here is that (ii) is much better. We first indicate some situations for which (when all the factors are restricted to a cuboidal region) the factorial approach is optimal, as judged by the |X′X| criterion, but the assumed models are often not sensible ones in practical work. We then examine what (similarly restricted) designs are optimal under the |X′X| criterion for the standard linear models of first and second order; because of the very rapid increase in computational difficulties, we consider only “cube plus star” type designs fork≥ 3 (except fork= 3,n= 10). In spite of computational requirements, we recommend use of the |X′X| criterion in general rather than the indiscriminate use of factorials and we briefly discuss the reasons why, both for linear and nonlinear model situations.
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