Mixed-level designs with resolution III or IV containing clear two-factor interaction components

详细信息    查看全文

• 作者：Qianqian Zhao ; Shengli Zhao
• 关键词：Mixed ; level designs ; Resolution ; Clear ; Two ; factor interaction components ; 62K15 ; 62K05
• 刊名：Metrika
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：78
• 期：8
• 页码：953-965
• 全文大小：439 KB
• 参考文献：Addelman S (1962) Orthogonal main-effect plans for asymmetrical factorial experiments. Technometrics 4:21鈥?6MATH MathSciNet CrossRef
  Ai MY, Zhang RC (2004) \(s^{n-m}\) designs containing clear main effects or clear two-factor interactions. Stat Probab Lett 69:151鈥?60MATH MathSciNet CrossRef
  Chen BJ, Li PF, Liu MQ, Zhang RC (2006) Some results on blocked regular 2-level fractional factorial designs with clear effects. J Stat Plan Inference 136:4436鈥?449MATH MathSciNet CrossRef
  Chen H, Hedayat AS (1998) \(2^{n-m}\) designs with resolution \({\rm III}\) and \({\rm IV}\) containing clear two-factor interactions. J Stat Plan Inference 75:147鈥?58MATH MathSciNet CrossRef
  Ke W, Tang B, Wu H (2005) Compromise plans with clear two-factor interactions. Stat Sin 15:709鈥?15MATH MathSciNet
  Li PF, Chen BJ, Liu MQ, Zhang RC (2006) A note on minimum aberration and clear criteria. Stat Probab Lett 76:1007鈥?011MATH MathSciNet CrossRef
  Mukerjee R, Wu CFJ (2006) A modern theory of factorial designs, Springer Series in Statistics. Springer, New York
  Tang B, Ma F, Ingram D, Wang H (2002) Bounds on the maximum number of clear two-factor interactions for \(2^{m-p}\) designs of resolution III and IV. Can J Stat 30:127鈥?36MATH MathSciNet CrossRef
  Wu CFJ (1989) Construction of \(2^m4^n\) designs via a grouping scheme. Ann Stat 17:1880鈥?885MATH CrossRef
  Wu CFJ, Chen Y (1992) A graph-aided method for planning two-level experiments when certain interactions are important. Technometrics 34:162鈥?75CrossRef
  Wu CFJ, Hamada M (2000) Experiments: planning, analysis and parameter design optimization. Wiley, New York
  Wu CFJ, Hamada M (2009) Experiments: planning, analysis and parameter design optimization, 2nd edn. Wiley, New York
  Wu CFJ, Zhang RC (1993) Minimum aberration designs with two-level and four-level factors. Biometrika 80:203鈥?09MATH MathSciNet
  Wu CFJ, Zhang RC, Wang R (1992) Construction of asymmetrical orthogonal arrays of the type \( OA(s^k, s^m(s^{r_1})^{n_1}\ldots (s^{r_t})^{n_t})\) . Stat Sin 2:203鈥?19MATH MathSciNet
  Wu H, Wu CFJ (2002) Clear two-factor interactions and minimum aberration. Ann Stat 30:1496鈥?511MATH CrossRef
  Yang GJ, Liu MQ, Zhang RC (2005) Weak minimum aberration and maximum number of clear two-factor interactions in \(2^{m-p}_{IV}\) designs. Sci China Ser A 48:1479鈥?487MATH MathSciNet CrossRef
  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 Plan Inference 136:4450鈥?458MATH MathSciNet CrossRef
  Zhao SL, Chen XF (2012a) Mixed two- and four-level fractional factorial split-plot designs with clear effects. J Stat Plan Inference 142:1789鈥?793MATH CrossRef
  Zhao SL, Chen XF (2012b) Mixed-level fractional factorial split-plot designs containing clear effects. Metrika 75:953鈥?62MATH MathSciNet CrossRef
  Zhao SL, Li PF, Liu MQ (2013) On blocked resolution IV designs containing clear two-factor interactions. J Complex 29:389鈥?95MATH MathSciNet CrossRef
  Zhao SL, Zhang RC (2008) \(2^{m}4^{n}\) designs with resolution III or IV containing clear two-factor interaction components. Stat Pap 49:441鈥?54MATH CrossRef
  Zhao SL, Zhang RC, Liu MQ (2008) Some results on \(4^m2^n\) designs with clear two-factor interaction components. Sci China Ser A 51:1297鈥?314MATH MathSciNet CrossRef
  Zi XM, Liu MQ, Zhang RC (2007) Asymmetrical designs containing clear effects. Metrika 65:123鈥?31MATH MathSciNet CrossRef
  
• 作者单位：Qianqian Zhao (1)
  Shengli Zhao (1)
  
  1. School of Statistics, Qufu Normal University, Qufu, 273165, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Probability Theory and Stochastic Processes
  Economic Theory
  
• 出版者：Physica Verlag, An Imprint of Springer-Verlag GmbH
• ISSN：1435-926X

文摘

Mixed-level designs are widely used in factorial experiments. Clear effects criterion is one of the important rules for selecting optimal fractional factorial designs. It is highly desirable to know when mixed-level designs with resolution III or IV can have clear two-factor interaction components. This paper considers mixed-level designs with one or two high-level factors and some two-level factors, denoted as \((2^{r})\times 2^n\) and \((2^{r_1})\times (2^{r_2})\times 2^n\), respectively, and gives a complete classification of the existence of clear two-factor interaction components in such designs with resolution III or IV. The results reveal the structures of these designs. Keywords Mixed-level designs Resolution Clear Two-factor interaction components