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Original Articles

Lower-order confounding information of inverse Yates-order two-level designs

, &
Pages 924-941 | Received 31 Aug 2017, Accepted 21 Nov 2018, Published online: 22 Jan 2019

References

  • Ai, M. Y., and R. C. Zhang. 2004. sn−m designs containing clear main effects or clear two-factor interactions. Statistics & Probability Letters 69:151–60. doi: 10.1016/j.spl.2004.06.015.
  • Berger, P. D. 1972. On Yates’ order in fractional factorial designs. Technometrics 14 (4):971–2. doi: 10.2307/1267146.
  • Box, G. E. P., and J. S. Hunter. 1961. The 2k−p fractional factorial designs. Technometrics 3: 311–51 and 449–58. doi: 10.2307/1266553.
  • Box, G. E. P., W. G. Hunter, and J. S. Hunter. 1978. Statistics for experimenters. New York: John Wiley.
  • Chen, H. G., and A. S. Hedayat. 1998. 2n−m Designs with resolution III or IV containing clear two-factor interactions. Journal of Statistical Planning Inference 75:147–58. doi: 10.1016/S0378-3758(98)00122-0.
  • Chen, J., and M. Q. Liu. 2011. Some theory for constructing general minimum lower-order confounding designs. Statistica Sinica 21:1541–55.
  • Chen, J., D. X. Sun, and C. F. J. Wu. 1993. A catalogue of two-level and three-level fractional factorial designs with small runs. International Statistical Review 61(1):131–45. doi: 10.2307/1403599.
  • Chen, J., and C. F. J. Wu. 1991. Some results on sn−k fractional factorial designs with minimum aberration of optimal moments. Annals of Statistics 2:1028–41.
  • Cheng, C. S., and R. Mukerjee. 1998. Regular fractional factorial designs with minimum aberration and maximum estimation capacity. The Annals of Statistics 26 :2289–300. doi: 10.1214/aos/1024691471.
  • Cheng, C. S., D. M. Steinberg, and D. X. Sun. 1999. Minimum aberration and model robustness for two-level fractional factorial designs. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 61 (1):85–93. doi: 10.1111/1467-9868.00164.
  • Cheng, C. S., and B. X. Tang. 2005. A general theory of minimum aberration and its applications. The Annals of Statistics 33 (2):944–58. doi: 10.1214/009053604000001228.
  • Cheng, Y., and R. C. Zhang. 2010. On construction of general minimum lower order confounding 2n−mdesigns with N/4+1≤n≤9N/32. Journal of Statistical Plann. Inference 140:2384–94. doi: 10.1016/j.jspi.2010.02.006.
  • Franklin, M. F. 1984. Constructing tables of minimum aberration pn−m designs. Technometrics 26:225–32. doi: 10.2307/1267548.
  • Fries, A., and W. G. Hunter. 1980. Minimum aberration 2k−p designs. Technometrics 22:601–8. doi: 10.2307/1268198.
  • Guo, B., Q. Zhou, and R. C. Zhang. 2014. Some results on constructing general minimum lower order confounding 2n−m designs for n≤2n−m−2. Metrika 77:721–32.
  • Li, P. F., S. L. Zhao, and R. C. Zhang. 2011. A theory on constructing 2n−m designs with general minimum lower order confounding. Statistica Sinica 21:1571–89.
  • Li, Z. M., Z. D. Teng, T. F. Zhang, and R. C. Zhang. 2016. Analysis on sn−m designs with general minimum lower-order confounding. AStA-Advances in Statistical Analysis 100:207–22.
  • Li, Z. M., and R. C. Zhang. 2015. Results for two-level designs with general minimum lower-order confounding. Scientific World J 2015:1–9. doi: 10.1155/2015/163234.
  • Li, Z. M., T. F. Zhang, and R. C. Zhang. 2013. Three-level regular designs with general minimum lower-order confounding. Canadian Journal of Statistics 41:192–210. doi: 10.1002/cjs.11154.
  • Li, Z. M., S. L. Zhao, and R. C. Zhang. 2015. On general minimum lower order confounding for s-level regular designs. Statistical & Probability Letters 99:202–9.
  • Mukerjee, R., and C. F. J. Wu. 2006. A modern theory of factorial designs. Springer Science Business Media Inc., New York.
  • Suen, C. Y., H. G. Chen, and C. F. J. Wu. 1997. Some identities on qn−m designs with application to minimum aberration designs. The Annals of Statistics 25:1176–88. doi: 10.1214/aos/1069362743.
  • Sun, D. X. 1993. Estimation cSapacity and related topics in experimental designs. Ph.D. dissertation. University of Waterloo, Waterloo.
  • Tang, B. X., F. S. Ma, D. Ingram, and H. Wang. 2002. Bounds on the maximum number of clear two-factor interactions for 2m−p designs of resolution III and IV. Canadian Journal of Statistics 30:127–36. doi: 10.2307/3315869.
  • Wu, C. F. J., and Y. Chen. 1992. A graph-aided method for planning two-level experiments when certain interactions are important. Technometrics 34:162–75. doi: 10.1080/00401706.1992.10484905.
  • Xu, H. Q., and Q. S. Cheng. 2008. A complementary design theory of doubling. The Annals of Statistics 36:445–57. doi: 10.1214/009005360700000712.
  • Zhang, R. C., and Y. Cheng. 2010. General minimum lower order confounding designs: an overview and a construction theory. Journal of Statistical and Planning Inference 140(7):1719–30. doi: 10.1016/j.jspi.2009.12.024.
  • Zhang, R. C., P. Li, S. L. Zhao, and M. Y. Ai. 2008. A general minimum lower-order confounding criterion for two-level regular designs. Statistica Sinica 18:1689–705.
  • Zhang, R. C., and R. Mukerjee. 2009a. Characterization of general minimum lower order confounding via complementary sets. Statistica Sinica 19:363–75.
  • Zhang, R. C., and R. Mukerjee. 2009b. General minimum lower order confounding in block designs using complementary sets. Statistica Sinica 19:1787–802.
  • Zhao, S. L., P. F. Li, R. C. Zhang, and R. Karunamuni. 2013. Construction of blocked two-level regular designs with general minimum lower order confounding. Journal of Statistical and Planning Inference 143:1082–90. doi: 10.1016/j.jspi.2012.12.011.
  • Zhao, S. L., P. F. Li, and M. Q. Liu. 2013. On blocked resolution IV designs containing clear two-factor interactions. Journal of Complexity 29(5):389–95. doi: 10.1016/j.jco.2013.04.002.
  • Zhao, S. L., D. K. J. Lin, and P. F. Li. 2016. A note on the construction of blocked two-level designs with general minimum lower order confounding. Journal of Statistical and Planning Inference 172:16–22. doi: 10.1016/j.jspi.2015.12.007.
  • Zhao, S. L., and Q. Sun. 2017. On constructing general minimum lower order confounding two-level block designs. Communications in Statistics – Theory and Methods 46(3):1261–74. doi: 10.1080/03610926.2015.1014112.
  • Zhao, S. L., and R. C. Zhang. 2008. Bound on the maximum number of clear two-factor interactions for 2n−(n−k) designs. Acta Mathematica Scientia 28:949–54.
  • Zhao, S. L., and Q. Q. Zhao. 2018. Some results on constructing two-level block designs with general minimum lower order confounding. Communications in Statistics – Theory and Methods 47(9):2227–37. doi: 10.1080/03610926.2017.1337148.
  • Zhao, Y. N., S. L. Zhao, and M. Q. Liu. 2016. A theory on constructing blocked two-level designs with general minimum lower order confounding. Frontiers of Mathematics in China 11(1):207–35. doi: 10.1007/s11464-015-0484-9.
  • Zhao, Y. N., S. L. Zhao, and M. Q. Liu. 2018. On construction of optimal two-level designs with multi block variables. Journal of System Science & Complexity 31(3):773–86. doi: 10.1007/s11424-017-6144-2.

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