Publication Cover
Statistics
A Journal of Theoretical and Applied Statistics
Volume 57, 2023 - Issue 3
118
Views
1
CrossRef citations to date
0
Altmetric
Research Article

Uniformity and projection uniformity of combined designs

ORCID Icon, &
Pages 515-533 | Received 15 Aug 2022, Accepted 19 Apr 2023, Published online: 25 Apr 2023

References

  • Box G, Hunter JS. The 2k−p fractional factorial designs part. Technometrics. 1961;3(3):311–351.
  • Fries A, Hunter WG. Minimum aberration 2k−p designs. Technometrics. 1980;22(4):601–608.
  • Ai MY, Hickernell FJ, Lin DKJ. Optimal foldover plans for regular s-level fractional factorial designs. Statist Probab Lett. 2008;78(7):896–903.
  • Li F, Jacroux M. Optimal foldover plans for blocked 2m−k fractional factorial designs. J Stat Plan Inference. 2007;137(7):2439–2452.
  • Li H, Mee RW. Better foldover fractions for resolution III 2k−p designs. Technometrics. 2002;44(3):278–283.
  • Li PF, Liu MQ, Zhang RC. Choice of optimal initial designs in sequential experiments. Metrika. 2005;61(2):127–135.
  • Li W, Lin DKJ. Optimal foldover plans for two-level fractional factorial designs. Technometrics. 2003;45(2):142–149.
  • Li W, Lin DKJ, Ye KQ. Optimal foldover plans for two-level non-regular orthogonal designs. Technometrics. 2003;45(4):347–351.
  • Li WL, Guo B, Huang HZ, et al. Semifoldover plans for three-level orthogonal arrays with quantitative factors. Statist. Papers. 2021;62(6):2691–2709.
  • Montgomery DC, Runger GC. Foldover of 2k−p resolution IV experimental designs. J Qual Technol. 1996;28(4):446–450.
  • Wang B, Robert GM, John FB. A note on the selection of optimal foldover plans for 16- and 32-run fractional factorial designs. J Stat Plan Inference. 2010;140(6):2337–2357.
  • Ye KQ, Li W. Some properties of blocked and unblocked foldover of 2k−p designs. Stat Sin. 2003;13:403–408.
  • Fang KT, Liu MQ, Qin H, et al. Theory and application of uniform experimental designs. Singapore: Springer; 2018.
  • Fang KT, Lin DKJ, Qin H. A note on optimal foldover design. Statist Probab Lett. 2003;62(3):245–250.
  • Lei YJ, Qin H, Zou N. Some lower bounds of centered L2-discrepancy on foldover designs. Acta Math Sci. 2010;31A(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(4):793–800.
  • Ou ZJ, Chatterjee K, Qin H. Lower bounds of various discrepancies on combined designs. Metrika. 2011;74(1):109–119.
  • Ou ZJ, Li HY. A new foldover strategy and optimal foldover plans for three-level design. Statist Papers. 2021;62(5):2433–2451.
  • Ou ZJ, Qin H. Optimal foldover plans of asymmetric factorials with minimum wrap-around L2-discrepancy. Statist Papers. 2019;60(5):1699–1716.
  • 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 Statistics-Theory Methods. 2014;43(10–12):2274–2285.
  • Ou ZJ, Qin H, Cai X. Optimal foldover plans of three-level designs with minimum wrap-around L2-discrepancy. Sci China Math. 2015;58(7):1537–1548.
  • Qin H, Chatterjee K, Ou ZJ. A lower bound for the centered L2-discrepancy on combined designs under the asymmetric factorials. Statistics. 2013;47(5):992–1002.
  • Ma CX, Fang KT, Lin DK. A note on uniformity and orthogonality. J Stat Plan Inference. 2003;113(1):323–334.
  • Fang KT, Qin H. Uniformity pattern and related criteria for two-level factorials. Sci China Ser A: Math. 2005;48(1):1–11.
  • Qin H, Chatterjee K. Lower bounds for the uniformity pattern of asymmetric fractional factorials. Communications in Statistics-Theory and Methods. 2009;38(9):1383–1392.
  • Qin H, Wang ZH, Chatterjee K. Uniformity pattern and related criteria for q-level factorials. J Stat Plan Inference. 2012;142(5):1170–1177.
  • Qin H, Wang ZH, Chatterjee K. Uniformity pattern of asymmetric fractional factorials. J Syst Sci Complexity. 2016;29(2):499–510.
  • Qin H, Zou N, Zhang SL. Design efficiency for minimum projection uniformity designs with two levels. J Syst Sci Complexity. 2011;24(4):761–768.
  • Song S, Qin H. Application of minimum projection uniformity criterion in complementary designs. Acta Math Sci. 2010;30B(1):180–186.
  • Wang ZH, Qin H. Uniformity pattern and related criteria for mixed-level designs. Commun Statist-Theory Methods. 2018;47(13):3192–3203.
  • Zhang SL, Qin H. Minimum projection uniformity criterion and its application. Statist Probab Lett. 2006;76(6):634–640.
  • Zhou YD, Fang KT, Ning JH. Mixture discrepancy for quasi-random point sets. J Complex. 2013;29(3–4):283–301.
  • Tang Y, Xu HQ, Lin DKJ. Uniform fractional factorial designs. Ann Statist. 2012;40(2):891–907.
  • Zhou YD, Xu HQ. Space-filling fractional factorial designs. J Am Stat Assoc. 2014;109(507):1134–1144.
  • Chen W, Qi ZF, Zhou YD. Constructing uniformity designs under mixture discrepancy. Statist Probab Lett. 2015;97:76–82.
  • Yi SY, Zhou YD. Projection uniformity under mixture discrepancy. Statist Probab Lett. 2018;140:96–105.
  • Wang K, Ou ZJ, Liu JQ, et al. Uniformity pattern of q-level factorials under mixture discrepancy. Statist Papers. 2021;62(4):1777–1793.
  • Wang K, Qin H, Ou ZJ. Uniformity pattern of mixed two- and three-level factorials under average projection mixture discrepancy. Statistics. 2022;56(1):121–133.
  • Hu LP, Chatterjee K, Liu JQ, et al. New lower bound for Lee discrepancy of asymmetrical factorials. Statist. Papers. 2020;61(4):1763–1772.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.