Abstract
The asymmetrical or mixed-level factorial design is a kind of important design in practice. There is a natural problem on how to choose an optimal (s 2)s n design for the practical need, where s is any prime or prime power. This paper considers the clear effects criterion for selecting good designs. It answers the questions of when an (s 2)s n design with fixed number of runs contains clear two-factor interaction (in brief 2fi) components and when it contains clear main effects or clear 2fis. It further gives the complete classification of (s 2)s n designs according to the clear 2fi components, main effects and 2fis they have.
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References
Addelman S (1962) Orthogonal main effect plans for asymmetrical factorial experiments. Technometrics 4:21–46
Ai MY, Zhang RC (2004) s n-m designs containing clear main effects or clear two-factor interactions. Stat Prob Lett 69:151–160
Chen H, Hedayat AS (1998) 2n-l designs with resolution III or IV containing clear two-factor interactions. J Stat Plann Inference 75:147–158
Chen BJ, Li PF, Liu MQ, Zhang RC (2006) Some results on blocked regular 2-level fractional factorial designs with clear effects. J Stat Plann Inference, available online
Fries A, Hunter WG (1980) Minimum aberration 2k-p designs. Technometrics 22:601–608
Ke W, Tang B, Wu H (2005) Compromise plans with clear two-factor interactions. Stat Sinica 15:709–715
Li PF, Chen BJ, Liu MQ, Zhang RC (2006a) A note on minimum aberration and clear criteria. Stat Prob Lett, available online
Li PF, Liu MQ, Zhang RC (2006b) 2m 41 designs with minimum aberration or weak minimum aberration. Stat Papers (to appear)
Mukerjee R, Wu CFJ (2001) Minimum aberration designs for mixed factorials in terms of complementary sets. Stat Sinica 11:225–239
Tang B, Ma F, Ingram D, Wang H (2002) Bounds on the maximum number of clear two-factor interactions for 2m-p designs of resolution III and IV. Can J Stat 30:127–136
Wu CFJ, Chen Y (1992) A graph-aided method for planning two-level experiments when certain interactions are improtant. Technometrics 34:162–175
Wu H, Wu CFJ (2002) Clear two-factor interactions and minimum aberration. Ann Stat 30:1496–1511
Wu CFJ, Zhang RC (1993) Minimum aberration designs with two-level and four-level factors. Biometrika 80:203–209
Wu CFJ, Zhang RC, Wang RG (1992) Construction of asymmetrical orthogonal arrays of the type \(OA(s^k, (s^{r_1})^{n_1}\cdots (s^{r_t})^{n_t})\). Stat Sinica 2:203–219
Yang GJ, Liu MQ, Zhang RC (2005) Weak minimum aberration and maximum number of clear two-factor interactions in \(2_{\rm IV}^{m-p}\) designs. Sci China Ser A 48:1479–1487
Yang JF, Li PF, Liu MQ, Zhang RC (2006) \(2^{(n_1+n_2)-(k_1+k_2)}\) fractional factorial split-plot designs containing clear effects. J Stat Plann Inference, available online
Zhang RC, Shao Q (2001) Minimum aberration (s 2)s n-k designs. Stat Sinica 11:213–223
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Zi, XM., Liu, MQ. & Zhang, RC. Asymmetrical Factorial Designs Containing Clear Effects. Metrika 65, 123–131 (2007). https://doi.org/10.1007/s00184-006-0064-9
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DOI: https://doi.org/10.1007/s00184-006-0064-9