Abstract
Fractional factorial designs have played a prominent role in the theory and practice of experimental design. For designs with qualitative factors under an ANOVA model, the minimum aberration criterion has been frequently used; however, for designs with quantitative factors, a polynomial regression model is often established, thus the β-wordlength pattern can be employed to compare different fractional factorial designs. Although the β-wordlength pattern was introduced in 2004, its properties have not been investigated extensively. In this paper, we will present some properties of β-wordlength pattern for four-level designs. These properties can help find better designs with quantitative factors.
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Cheng, S. W., Wu, C. F. J.: Factor screening and response surface exploration (with discussion). Statist. Sinica, 11, 553–604 (2001)
Cheng, S. W., Ye, K. Q.: Geometric isomorphism and minimum aberration for factorial designs with quantitative factors. Ann. Statist., 32, 2168–2185 (2004)
Deng, L. Y., Tang, B.: Generalized resolution and minimum aberration criteria for Plackett-Burman and other nonregular factorial designs. Statist. Sinica, 9, 1071–1082 (1999)
Draper, N. R., Smith, H.: Applied Regression Analysis (3rd Edition), Wiley, New York, 1998
Fang, K. T., Ma, C. X.: Uniform and Orthogonal Designs (in Chinese), Science Press, Beijing, 2001
Fries, A., Hunter, W. G.: Minimum aberration 2k-p designs. Technometrics, 22, 601–608 (1980)
Ma, C. X., Fang, K. T.: A note on generalized aberration in factorial designs. Metrika, 53, 85–93 (2001)
Mukerjee, R., Wu, C. F. J.: A Modern Theory of Factorial Design, Springer, New York, 2006
Pang, F., Liu, M. Q.: Indicator function based on complex contrasts and its application in general facotrial designs. J. Statist. Plann. Inference, 140, 189–197 (2010)
Tang, B., Deng, L. Y.: Minimum G 2-aberration for nonregular fractional factorial designs. Ann. Statist., 27, 1914–1926 (1999)
Tang, Y., Xu, H.: Permuting regular fractional factorial designs for screening quantitative factors. Biometrika, 101, 333–350 (2014)
Wu, C. F. J., Hamada, M.: Experiments: Planning, Analysis and Parameter Design Optimization (2nd Edition), Wiley, New York, 2009
Xu, H., Wu, C. F. J.: Generalized minimum aberration for asymmetrical fractional factorial designs. Ann. Statist., 29, 1066–1077 (2001)
Zhang, R. C., Li, P., Zhao, S. L., et al.: A general minimum lower-order confounding criterion for two-level regular designs. Statist. Sinica, 18, 1689–1705 (2008)
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Supported by NSFC (Grant No. 11271279), NSF of Jiangsu Province (Grant No. BK2012612) and Qing Lan Project
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Sheng, W.W., Li, X.M. & Tang, Y. Some properties of β-wordlength pattern for four-level designs. Acta. Math. Sin.-English Ser. 31, 1163–1170 (2015). https://doi.org/10.1007/s10114-015-3616-y
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DOI: https://doi.org/10.1007/s10114-015-3616-y