Classification Rule for Optimal Blocking for Nonregular Factorial Designs

Title & Authors
Classification Rule for Optimal Blocking for Nonregular Factorial Designs
Park, Dong-Kwon; Kim, Hyoung-Soon; Kang, Hee-Kyoung;

Abstract
In a general fractional factorial design, the n-levels of a factor are coded by the $\small{n^{th}}$ roots of the unity. Pistone and Rogantin (2007) gave a full generalization to mixed-level designs of the theory of the polynomial indicator function using this device. This article discusses the optimal blocking scheme for nonregular designs. According to hierarchical principle, the minimum aberration (MA) has been used as an important criterion for selecting blocked regular fractional factorial designs. MA criterion is mainly based on the defining contrast groups, which only exist for regular designs but not for nonregular designs. Recently, Cheng et al. (2004) adapted the generalized (G)-MA criterion discussed by Tang and Deng (1999) in studying $\small{2^p}$ optimal blocking scheme for nonregular factorial designs. The approach is based on the method of replacement by assigning $\small{2^p}$ blocks the distinct level combinations in the column with different blocks. However, when blocking level is not a power of two, we have no clue yet in any sense. As an example, suppose we experiment during 3 days for 12-run Plackett-Burman design. How can we arrange the 12-runs into the three blocks? To solve the problem, we apply G-MA criterion to nonregular mixed-level blocked scheme via the mixed-level indicator function and give an answer for the question.
Keywords
Aliasing;indicator function;minimum aberration;nonregular design;wordlength pattern;
Language
English
Cited by
References
1.
Cheng, S. W., Li, W. and Ye, K. Q. (2004). Blocked nonregular two-level factorial designs. Technometrics, 46, 269-279

2.
Cheng, S. W. and Wu, C. F. J. (2002). Choice of optimal blocking schemes in two-level and three-level designs. Technometrics, 44, 269-277

3.
Deng, L. Y. and Tang, B. (2002). Design selection and classification for Hadamard matrices using generalized minimum aberration criteria. Technometric, 44, 173-184

4.
Fries, A. and Hunter, W. G. (1980). Minimum aberration \$2^{n-p}\$ designs. Technometrics, 26, 225-232

5.
Hamada, M. and Wu, C. F. J. (1992). Analysis of designed experiments with complex aliasing. Journal of Quality Technology, 24, 130-137

6.
Pistone, G. and Rogantin, M. P. (2007). Indicator function and complex coding for mixed fractional factorial designs. Journal of Statistical Planning and Inference, in press

7.
Tang, B. and Deng, L. Y. (1999). Minimum G2-aberration for nonregular fractional factorial designs. The Annals of Statistics, 27, 1914-1926

8.
Wu, C. F. J. and Zhang, R. C. (1993). Minimum aberration designs with two-level and fourlevel factors. Biometrika, 80, 203-209

9.
Ye, K. Q. (2003). Indicator function and its application in two-level factorial designs. The Annals of Statistics, 31, 984-994

10.
Zhang, R. C. and Park, D. K. (2000). Optimal blocking oftwo-level fractional factorial designs. Journal of Statistical Planning and Inference, 91, 107-121