Analysis on \(s^{n-m}\) designs with general minimum lower-order confounding

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• 作者：Zhiming Li ; Zhidong Teng ; Tianfang Zhang…
• 关键词：s ; level design ; Component effect hierarchy principle ; Aliased component ; number pattern ; General minimum lower ; order confounding ; GMC design ; Complementary set
• 刊名：AStA Advances in Statistical Analysis
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：100
• 期：2
• 页码：207-222
• 全文大小：485 KB
• 参考文献：Ai, M.Y., Zhang, R.C.: \(s^{n-m}\) designs containing clear main effects or two-factor interactions. Stat. Probab. Lett. 69, 151–160 (2004)MathSciNet CrossRef MATH
  Box, G.E.P., Hunter, J.S.: The \(2^{k-p}\) fractional factorial designs I and II. Technometrics 3, 311–351 and 449–458 (1961)
  Box, G.E.P., Hunter, W.G., Hunter, J.S.: Statistics for Experimenters. Wiley, New York (1978)MATH
  Chen, H., Hedayat, A.S.: \(2^{n-l}\) designs with resolution III or IV containing clear two-factor interactions. J. Stat. Plan. Inference 75, 147–158 (1998)MathSciNet CrossRef MATH
  Chen, J., Liu, M.Q.: Some theory for constructing general minimum lower order confounding designs. Stat. Sin. 21, 1541–1555 (2011)MathSciNet MATH
  Cheng, C.S., Mukerjee, R.: Regular fractional factorial designs with minimum aberration and maximum estimation capacity. Ann. Stat. 26, 2289–2300 (1998)MathSciNet CrossRef MATH
  Cheng, C.S., Steinberg, D.M., Sun, D.X.: Minimum aberration and model robustness for two-level fractional factorial designs. J. Roy. Stat. Soc. B 61, 85–93 (1999)MathSciNet CrossRef MATH
  Cheng, Y., Zhang, R.C.: On construction of general minimum lower order confounding \(2^{n-m}\) designs with \(N/4+1\le n\le 9N/32\) . J. Stat. Plan. Inference 140, 2384–2394 (2010)CrossRef MATH
  Dean, A.M., Voss, D.T.: Design and Analysis of Experiments. Springer, New York (1999)CrossRef MATH
  Fries, A., Hunter, W.G.: Minimum aberration \(2^{k-p}\) designs. Technometrics 22, 601–608 (1980)MathSciNet MATH
  Hu, J.W., Zhang, R.C.: Some results on two-level regular designs with general minimum lower order confounding. J. Stat. Plan. Inference 141, 1774–1782 (2011)MathSciNet CrossRef MATH
  Li, P.F., Zhao, S.L., Zhang, R.C.: A theory on constructing \(2^{n-m}\) designs with general minimum lower order confounding. Stat. Sin. 21, 1571–1589 (2011)MathSciNet MATH
  Li, Z.M., Zhang, T.F., Zhang, R.C.: Three-level regular designs with general minimum lower-order confounding. Can. J. Stat. 41, 192–210 (2013)MathSciNet CrossRef MATH
  Montgomery, D.C.: Design and Analysis of Experiments. Wiley, New York (2001)
  Mukerjee, R., Wu, C.F.J.: A Modern Theory of Factorial Designs. Springer, New York (2006)MATH
  Sun, D.X.: Estimation capacity and related topics in experimental design. Univ. Waterloo. Ph.D. Thesis (1993)
  Tang, B., Ma, F., Ingram, D., Wang, H.: Bounds on the maximum number of clear two-factor interaction for \(2^{m-p}\) designs of resolution III and IV. Can. J. Stat. 30, 127–136 (2002)MathSciNet CrossRef MATH
  Wei, J.L., Yang, J.F., Li, P., Zhang, R.C.: Split-plot designs with general minimum lower-order confounding. Sci. China Math. 53, 939–952 (2010)MathSciNet CrossRef MATH
  Wu, C.F.J., Chen, Y.: A graph-aided method for planning two-level experiments when certain interactions are important. Technometrics 34, 162–175 (1992)CrossRef
  Wu, C.F.J., Hamada, M.: Experiments: Planning, Analysis, and Parameter Design Optimization. Wiley, New York (2009)MATH
  Zhang, R.C., Cheng, Y.: General minimum lower order confounding designs: an overview and a construction theory. J. Stat. Plan. Inference 140, 1719–1730 (2010)MathSciNet CrossRef MATH
  Zhang, R.C., Li, P., Zhao, S.L., Ai, M.Y.: A general minimum lower-order confounding criterion for two-level regular designs. Stat. Sin. 18, 1689–1705 (2008)MathSciNet MATH
  Zhang, R.C., Mukerjee, R.: Characterization of general minimum lower order confounding via complementary sets. Stat. Sin. 19, 363–375 (2009)MathSciNet MATH
  
• 作者单位：Zhiming Li (1)
  Zhidong Teng (1)
  Tianfang Zhang (2)
  Runchu Zhang (3) (4)
  
  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, China
  2. College of Mathematics and Information Sciences, Jiangxi Normal University, Nanchang, 330022, China
  3. KLAS and School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China
  4. LPMC and School of Mathematical Sciences, Nankai University, Tianjin, 300071, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Statistics
  Statistics
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Probability Theory and Stochastic Processes
  Econometrics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1863-818X

文摘

An optimal design should minimize the confounding among factor effects, especially the lower-order effects, such as main effects and two-factor interaction effects. Based on the aliased component-number pattern, general minimum lower-order confounding (GMC) criterion can provide the confounding information among factors of designs in a more elaborate and explicit manner. In this paper, we extend GMC theory to s-level regular designs, where s is a prime or prime power. For an \(s^{n-m}\) design D with \(N=s^{n-m}\) runs, the confounding of design D is given by complementary set. Further, according to the factor number n, we discuss two cases: (i) \(N/s<n\le (N-1)/(s-1)\), and (ii) \((N/s+1)/2<n\le N/s\). We not only provide the lower-order confounding information among component effects of D, but also obtain three necessary conditions for design D to have GMC.