Abstract
In the design of experiments, an optimal design should minimize the confounding between factorial effects, especially main effects and two-factor interaction effects. The general minimum lower-order confounding (GMC) criterion can be used to choose optimal regular designs based on the aliased component-number pattern. This paper aims to study the confounding properties of lower-order effects and provide several computer algorithms to calculate the lower-order confounding in regular designs. We provide a search algorithm to obtain GMC designs. Through python software, we conduct these algorithms. Some examples are analyzed to illustrate the effectiveness of the proposed algorithms.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Box GEP, Hunter JS (1961) The \(2^{k-p}\) fractional factorial designs. Technometrics 3(311–352):449–458
Chen J, Liu MQ (2011) Some theory for constructing general minimum lower order confounding design. Stat Sin 21(4):1541–1555
Cheng Y, Zhang RC (2010) 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
Fries A, Hunter WG (1980) Minimum aberration \(2^{k-p}\) designs. Technometrics 22:601–608
Guo B, Zhou Q, Zhang RC (2014) Some results on constructing general minimum lower order confounding \(2^{n-m}\) designs for \(n\le 2^{n-m-2}\). Metrika 77:721–732
Hu J, Zhang RC (2011) Some results on two-level regular designs with general minimum lower-order confounding. J Stat Plan Inference 141:1774–1782
Huang ZY, Li ZM, Zhang G, Chen T (2022) Lower-order confounding information of inverse Yates-order designs with three levels. Metrika. https://doi.org/10.1007/s00184-022-00876-z
Kong QX, Li ZM, Chen T, Zhang G (2023) Results on constructing sn-m regular designs with general minimum lower-order confounding. J Stat Plan Inference 222:122–131
Li PF, Zhao SL, Zhang RC (2011) A theory on constructing \(2^{n-m}\) designs with general minimum lower order confounding. Stat Sin 21:1571–1589
Li ZM, Zhang TF, Zhang RC (2013) Three-level regular designs with general minimum lower-order confounding. Can J Stat 41:192–210
Li ZM, Zhao SL, Zhang RC (2015) On general minimum lower order confounding criterion for s-level regular designs. Stat Probab Lett 99:202–209
Li ZM, Teng ZD, Zhang TF, Zhang RC (2016) Analysis on \(s^{n-m}\) designs with general minimum lower-order confounding. AStA-Adv Stat Anal 100:207–222
Li ZM, Teng ZD, Wu LJ, Zhang RC (2018) Construction of some \(3^{n-m}\) regular designs with general minimum lower order confounding. J Stat Theory Pract 12(2):336–355
Li ZM, Li MM, Zhao SL (2020) Lower-order confounding information of inverse Yates-order two-level designs. Commun Stat Theory Methods 49:924–941
Li ZM, Kong QX, Ai MY (2020) Construction of some \(s\)-level regular designs with general minimum lower-order confounding. Stat Probab Lett 167:108897
Cx MA, Fang KT (2001) A note on generalized aberration in factorial designs. Metrika 53:85–93
Mukerjee R, Wu CF (2006) A modern theory of factorial design. Springer, New York
Raghavarao D (1971) Constructions and combinatorial problems in design of experiments. Wiley, New York
Tang B, Deng LY (1999) Minimum G\(_2\)-aberration for nonregular fractional factorial designs. Ann Stat 27:1914–1926
Wei JL, Yang JF (2013) On simplifying the calculations leading to designs with general minimum lower-order confounding. Metrika 76:723–732
Wu CFJ, Chen Y (1992) A graph-aided method for planning two-level experiments when certain interactions are important. Technometrics 34:162–175
Xu H, Wu CFJ (2001) Generalized minimum aberration for asymmetrical fractional factorial designs. Ann Stat 29:1066–1077
Zhang RC, Cheng Y (2010) General minimum lower order confounding designs: an overview and a construction theory. J Stat Plan Inference 140:1719–1730
Zhang RC, Mukerjee R (2009) Characterization of general minimum lower order confounding via complementary sets. Stat Sin 19:363–375
Zhang RC, Li P, Zhao SL, Ai MY (2008) A general minimum lower-order confounding criterion for two-level regular designs. Stat Sin 18:1689–1705
Acknowledgements
We thank the editor and referees for their insightful comments and constructive suggestions. The work was supported by the National Natural Science Foundation of China (12061070) and the Natural Science Foundation of Xinjiang Uygur Autonomous Region (2021D01E13).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendix
Appendix
1.1 A: Python code of Design_ACNP
1.2 B: Python code of Search_GMC
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Li, Z., Li, Z. Computer algorithms of lower-order confounding in regular designs. Comput Stat 39, 653–676 (2024). https://doi.org/10.1007/s00180-022-01315-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00180-022-01315-3