IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v66y2004i1p51-57.html
   My bibliography  Save this article

Some results on generalized minimum aberration for symmetrical fractional factorial designs

Author

Listed:
  • Qin, Hong
  • Chen, Yin-Bao

Abstract

Generalized minimum aberration of fractional factorial designs has popularly been discussed. Recently, Lu et al. (Technical Report-324, 2002) proposed a so-called nearest balance criterion, which extends the V-criterion studied by Tang (Biometrika, 88 (2001) 401) for two-level designs to multi-level designs, to evaluate fractional factorials. In this paper, that generalized minimum aberration coincides with nearest balance for symmetrical factorials is reported, which is a generalization of the related results in Tang (2001). Our results not only further provide a projection interpretation of generalized minimum aberration in terms of level combinations but they also give a theoretical justification of the nearest balance criterion. A lower bound of generalized word length pattern for symmetrical factorials is also obtained.

Suggested Citation

  • Qin, Hong & Chen, Yin-Bao, 2004. "Some results on generalized minimum aberration for symmetrical fractional factorial designs," Statistics & Probability Letters, Elsevier, vol. 66(1), pages 51-57, January.
    • Handle: RePEc:eee:stapro:v:66:y:2004:i:1:p:51-57
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(03)00306-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kai-Tai Fang & Gen-Nian Ge & Min-Qian Liu & Hong Qin, 2003. "Construction of minimum generalized aberration designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 57(1), pages 37-50, February.
    2. C.‐S. Cheng & D. M. Steinberg & D. X. Sun, 1999. "Minimum aberration and model robustness for two‐level fractional factorial designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 85-93.
    3. Chen, Hegang, 1998. "Some projective properties of fractional factorial designs," Statistics & Probability Letters, Elsevier, vol. 40(2), pages 185-188, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhang, Shangli & Qin, Hong, 2006. "Minimum projection uniformity criterion and its application," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 634-640, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. A. M. Elsawah, 2021. "Multiple doubling: a simple effective construction technique for optimal two-level experimental designs," Statistical Papers, Springer, vol. 62(6), pages 2923-2967, December.
    2. Mike Jacroux, 2007. "Maximal Rank Minimum Aberration Foldover Plans for 2 m-k Fractional Factorial Designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 65(2), pages 235-242, February.
    3. Nguyen, Nam-Ky & Liu, Min-Qian, 2008. "An algorithmic approach to constructing mixed-level orthogonal and near-orthogonal arrays," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5269-5276, August.
    4. Yaquelin Verenice Pantoja-Pacheco & Armando Javier Ríos-Lira & José Antonio Vázquez-López & José Alfredo Jiménez-García & Martha Laura Asato-España & Moisés Tapia-Esquivias, 2021. "One Note for Fractionation and Increase for Mixed-Level Designs When the Levels Are Not Multiple," Mathematics, MDPI, vol. 9(13), pages 1-20, June.
    5. Zhang, Shangli & Qin, Hong, 2006. "Minimum projection uniformity criterion and its application," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 634-640, March.
    6. Minyang Hu & Shengli Zhao, 2022. "Minimum Aberration Split-Plot Designs Focusing on the Whole Plot Factors," Mathematics, MDPI, vol. 10(5), pages 1-12, February.
    7. Li, Peng-Fei & Liu, Min-Qian & Zhang, Run-Chu, 2004. "Some theory and the construction of mixed-level supersaturated designs," Statistics & Probability Letters, Elsevier, vol. 69(1), pages 105-116, August.
    8. Satoshi Aoki, 2010. "Some optimal criteria of model-robustness for two-level non-regular fractional factorial designs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(4), pages 699-716, August.
    9. SCHOEN, Eric D. & NGUYEN, Man V.M., 2007. "Enumeration and classification of orthogonal arrays," Working Papers 2007021, University of Antwerp, Faculty of Business and Economics.
    10. Angelopoulos, P. & Koukouvinos, C., 2007. "Maximum estimation capacity projection designs from Hadamard matrices with 32, 36 and 40 runs," Statistics & Probability Letters, Elsevier, vol. 77(2), pages 220-229, January.
    11. Peng-Fei Li & Min-Qian Liu & Run-Chu Zhang, 2007. "2 m 4 1 designs with minimum aberration or weak minimum aberration," Statistical Papers, Springer, vol. 48(2), pages 235-248, April.
    12. Li, Peng-Fei & Chen, Bao-Jiang & Liu, Min-Qian & Zhang, Run-Chu, 2006. "A note on minimum aberration and clear criteria," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 1007-1011, May.
    13. Chen, Jie & Liu, Min-Qian, 2008. "Optimal mixed-level supersaturated design with general number of runs," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2496-2502, October.
    14. Ai, Mingyao & Zhang, Runchu, 2004. "Multistratum fractional factorial split-plot designs with minimum aberration and maximum estimation capacity," Statistics & Probability Letters, Elsevier, vol. 69(2), pages 161-170, August.
    15. Fasheng Sun & Boxin Tang, 2017. "A Method of Constructing Space-Filling Orthogonal Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 683-689, April.
    16. Nairanjana Dasgupta & Mike Jacroux & Rita SahaRay, 2010. "Partially replicated fractional factorial designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(3), pages 295-311, May.
    17. Li, Zhiming & Zhao, Shengli & Zhang, Runchu, 2015. "On general minimum lower order confounding criterion for s-level regular designs," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 202-209.
    18. Ghosh, Subir & Tian, Ying, 2006. "Optimum two level fractional factorial plans for model identification and discrimination," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1437-1450, July.
    19. Qiming Bai & Hongyi Li & Shixian Zhang & Jiezhong Tian, 2023. "Design Efficiency of the Asymmetric Minimum Projection Uniform Designs," Mathematics, MDPI, vol. 11(3), pages 1-20, February.
    20. Grömping, Ulrike, 2014. "R Package FrF2 for Creating and Analyzing Fractional Factorial 2-Level Designs," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 56(i01).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:66:y:2004:i:1:p:51-57. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.