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A Journal of Theoretical and Applied Statistics
Volume 51, 2017 - Issue 3
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Original Articles

A closer look at de-aliasing effects using an efficient foldover technique

Pages 532-557 | Received 23 Oct 2015, Accepted 20 Jul 2016, Published online: 07 Oct 2016

References

  • Montgomery DC, Runger GC. Foldover of 2k−p resolution IV experimental designs. Qual Technol. 1996;28:446–450.
  • Li W, Lin DKJ. Optimal foldover plans for two-level fractional factorial designs. Technometrics. 2003;45:142–149. doi: 10.1198/004017003188618779
  • Li P-F, Liu M-Q, Zhang R-C. Choice of optimal initial designs in sequential experiments. Metrika. 2005;61:127–135. doi: 10.1007/s001840400327
  • Wang B, McLeod RG, Brewster JF. A note on the selection of optimal foldover plans for 16- and 32-run fractional factorial designs. J Statist Plann Inference. 2010;140:1497–1500. doi: 10.1016/j.jspi.2009.12.011
  • Cheong KTW, Htay K, Tan RHC, et al. Identifying combinatorial growth inhibitory effects of various plant extracts on leukemia cells through systematic experimental design. Amer J Plant Sci. 2012;3:1390–1398. doi: 10.4236/ajps.2012.310168
  • Fang K-T, Lin DKJ, Qin H. A note on optimal foldover design. Statist Probab Lett. 2003;62:245–250. doi: 10.1016/S0167-7152(03)00008-7
  • Elsawah AM, Qin H. Lee discrepancy on symmetric three-level combined designs. Statist Probab Lett. 2015;96:273–280. doi: 10.1016/j.spl.2014.09.027
  • Elsawah AM, Qin H. A new strategy for optimal foldover two-level designs. Statist Probab Lett. 2015;103:116–126. doi: 10.1016/j.spl.2015.04.020
  • Elsawah AM, Qin H. A new look on optimal foldover plans in terms of uniformity criteria. Commun Statist Theory Methods. 2016. Available from: http://dx.doi.org/10.1080/03610926.2015.1024862.
  • Elsawah AM, Qin H. An efficient methodology for constructing optimal foldover designs in terms of mixture discrepancy. J Korean Statist Soc. 2016;45:77–88. doi: 10.1016/j.jkss.2015.07.004
  • Elsawah AM, Al-awady MA, Abd Elgawad MA, et al. A note on optimal foldover four-level factorials. Acta Math Sin. 2016;32(3):286–296. doi: 10.1007/s10114-016-4749-3
  • Lei YJ, Qin H, Zou N. Some lower bounds of centered L2-discrepancy on foldover designs. Acta Math Sci. 2010;30A(6):1555–1561.
  • Lei YJ, Ou ZJ, Qin H, et al. A note on lower bound of centered L2-discrepancy on combined designs. Acta Math Sci. 2012;28:793–800. doi: 10.1007/s10114-011-0009-8
  • Ou ZJ, Chatterjee K, Qin H. Lower bounds of various discrepancies on combined designs. Metrika. 2011;74:109–119. doi: 10.1007/s00184-009-0292-x
  • Ou ZJ, Qin H, Cai X. A lower bound for the wrap-around L2-discrepancy on combined designs of mixed two- and three-level factorials. Commun Statist Theory Methods. 2014;43:2274–2285. doi: 10.1080/03610926.2013.776082
  • Ou ZJ, Qin H, Cai X. Optimal foldover plans of three level designs with minimum wrap-around L2-discrepancy. Sci China Math. 2015;58: 1537–1548. doi: 10.1007/s11425-014-4936-6.
  • Elsawah AM, Qin H. Optimum mechanism for breaking the confounding effects of mixed-level designs. Comput Stat. 2016. Available from: http://dx.doi.org/10.1007/s00180-016-0651-9.
  • Zhou Y-D, Ning J-H, Song X-B. Lee discrepancy and its applications in experimental designs. Statist Probab Lett. 2008;78:1933–1942. doi: 10.1016/j.spl.2008.01.062
  • Zhou Y-D, Fang K-F, Ning J-H. Mixture discrepancy for quasi-random point sets. J Complexity. 2013;29:283–301. doi: 10.1016/j.jco.2012.11.006
  • Hickernell FJ. A generalized discrepancy and quadrature error bound. Math Comput. 1998;67:299–322. doi: 10.1090/S0025-5718-98-00894-1
  • Hickernell FJ, Lattice rules: how well do they measure up? In: Hellekalek P, Larcher G, editors. Random and quasi-random point sets. New York: Springer; 1998. p. 109–166. (Lecture Notes in Statistics; 138).
  • Elsawah AM, Qin H. Asymmetric uniform designs based on mixture discrepancy. J App Statist. 2016. Available from: http://dx.doi.org/10.1080/02664763.2016.1140727.
  • Fang K-T, Maringer D, Tang Y, et al. Lower bounds and stochastic optimization algorithms for uniform designs with three or four levels. Math Comput. 2005;75:859–879. doi: 10.1090/S0025-5718-05-01806-5
  • Elsawah AM, Qin H. New lower bound for centered L2-discrepancy of four-level U-type designs. Statist Probab Lett. 2014;93:65–71. doi: 10.1016/j.spl.2014.06.008
  • Elsawah AM, Qin H. Lower bound of centered L2-discrepancy for mixed two and three levels U-type designs. J Statist Plann Inference. 2015;161:1–11. doi: 10.1016/j.jspi.2014.12.007
  • Elsawah AM, Qin H. An effective approach for the optimum addition of runs to three-level uniform designs. J Korean Statist Soc. 2016. Available from: http://dx.doi.org/10.1016/j.jkss.2016.05.003.
  • Zhang Q, Wang Z, Hu J, et al. A new lower bound for wrap-around L2-discrepancy on two and three mixed level factorials. Statist Probab Lett. 2015;96:133–140. doi: 10.1016/j.spl.2014.08.023
  • Chatterjee K, Li Z, Qin H. Some new lower bounds to centered and wrap-round L2-discrepancies. Statist Probab Lett. 2012;82(7):1367–1373. doi: 10.1016/j.spl.2012.03.011
  • Fang K-T, Mukerjee R. A connection between uniformity and aberration in regular fractions of two-level factorials. Biometrika. 2000;87:193–198. doi: 10.1093/biomet/87.1.193
  • Fang KT, Ma CX, Mukerjee R, Uniformity in fractional factorials. In: Fang KT, Hickernell FJ, Niederreiter H, editors. Monte Carlo and Quasi-Monte Carlo methods in scientific computing. Berlin: Springer-Verlag; 2002.
  • Elsawah AM, Qin H. Mixture discrepancy on symmetric balanced designs. Statist Probab Lett. 2015;104:123–132. doi: 10.1016/j.spl.2015.05.007
  • Zou N, Ren P, Qin H. A note on Lee discrepancy. Statist Probab Lett. 2009;79:496–500. doi: 10.1016/j.spl.2008.09.022
  • Chatterjee K, Qin H, Zou N. Lee discrepancy on two and three mixed level factorials. Sci China. 2012;55(3):663–670. doi: 10.1007/s11425-012-4366-2
  • Ke X, Zhang R, Ye H-J. Two- and three-level lower bounds for mixture L2-discrepancy and construction of uniform designs by threshold accepting. J Complexity. 2015. Available from: http://dx.doi.org/10.1016/j.jco.2015.01.002.

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