IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v76y2006i10p1007-1011.html
   My bibliography  Save this article

A note on minimum aberration and clear criteria

Author

Listed:
  • Li, Peng-Fei
  • Chen, Bao-Jiang
  • Liu, Min-Qian
  • Zhang, Run-Chu

Abstract

Minimum aberration and clear criteria are two important rules for selecting optimal fractional factorial designs, in both unblocked and blocked cases. In this paper, we first show that under some given conditions, a blocked design DB=(D,B) having blocked minimum aberration is equivalent to D having minimum aberration. Let m=n/4+1 and n=2q. From the results of Tang et al. [Bounds on the maximum number of clear two-factor interactions for 2m-p designs of resolution III and IV. Canad. J. Statist. 30 (2002) 127-136] and Wu and Wu [Clear two-factor interactions and minimum aberration. Ann. Statist. 30 (2002) 1496-1511], we know that the maximum number of clear two-factor interactions (2FIs) in designs is n/2-1. Here it is proved that the maximum number of clear 2FIs in 2m-(m-q) designs in 2l blocks, denoted by , is also n/2-1 when q-l[greater-or-equal, slanted]2. Furthermore, it is shown that any design that contains the maximum number of clear 2FIs is not a minimum aberration design, and this conclusion also holds when the design is a design with q-l[greater-or-equal, slanted]2.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:10:p:1007-1011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(05)00440-2
    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. 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.
    2. Fred J. Hickernell, 2002. "Uniform designs limit aliasing," Biometrika, Biometrika Trust, vol. 89(4), pages 893-904, December.
    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. Qianqian Zhao & Shengli Zhao, 2015. "Mixed-level designs with resolution III or IV containing clear two-factor interaction components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(8), pages 953-965, November.
    2. Xue-Min Zi & Min-Qian Liu & Run-Chu Zhang, 2007. "Asymmetrical Factorial Designs Containing Clear Effects," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 65(1), pages 123-131, February.

    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. 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.
    2. Yu, Jun & Meng, Xiran & Wang, Yaping, 2023. "Optimal designs for semi-parametric dose-response models under random contamination," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    3. Chatterjee, Kashinath & Qin, Hong, 2008. "A new look at discrete discrepancy," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2988-2991, December.
    4. 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.
    5. Hong Qin & Na Zou & Kashinath Chatterjee, 2009. "Connection between uniformity and minimum moment aberration," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 79-88, June.
    6. Fang Pang & Min-Qian Liu, 2012. "A note on connections among criteria for asymmetrical factorials," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(1), pages 23-32, January.
    7. 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.
    8. Mingyao Ai & Shuyuan He, 2006. "Interaction balance for symmetrical factorial designs with generalized minimum aberration," Statistical Papers, Springer, vol. 47(1), pages 125-135, January.
    9. E. Androulakis & C. Koukouvinos, 2013. "A new variable selection method for uniform designs," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(12), pages 2564-2578, December.
    10. 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.
    11. Li, Hongyi & Chatterjee, Kashinath & Li, Bo & Qin, Hong, 2016. "Construction of Sudoku-based uniform designs with mixed levels," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 111-118.
    12. Yao Xiao & Hong Qin & Kashinath Chatterjee & Na Zou, 2024. "Theory and application of absolute discrepancy in experimental designs," Statistical Papers, Springer, vol. 65(9), pages 5775-5795, December.
    13. 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.
    14. 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.
    15. 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.
    16. Narayanaswamy Balakrishnan & Hong Qin & Kashinath Chatterjee, 2016. "Generalized projection discrepancy and its applications in experimental designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(1), pages 19-35, January.
    17. 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.
    18. 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.
    19. Yang Huang & Yongdao Zhou, 2022. "Convergence of Uniformity Criteria and the Application in Numerical Integration," Mathematics, MDPI, vol. 10(19), pages 1-20, October.
    20. Biao Luo & Hongyi Li & Yingying Wei & Zujun Ou, 2022. "Uniform design with prior information of factors under weighted wrap-around $$L_2$$ L 2 -discrepancy," Computational Statistics, Springer, vol. 37(5), pages 2717-2739, November.

    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:76:y:2006:i:10:p:1007-1011. 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.