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Minimum aberration and model robustness for two‐level fractional factorial designs

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  • C.‐S. Cheng
  • D. M. Steinberg
  • D. X. Sun

Abstract

The performance of minimum aberration two‐level fractional factorial designs is studied under two criteria of model robustness. Simple sufficient conditions for a design to dominate another design with respect to each of these two criteria are derived. It is also shown that a minimum aberration design of resolution III or higher maximizes the number of two‐factor interactions which are not aliases of main effects and, subject to that condition, minimizes the sum of squares of the sizes of alias sets of two‐factor interactions. This roughly says that minimum aberration designs tend to make the sizes of the alias sets very uniform. It follows that minimum aberration is a good surrogate for the two criteria of model robustness that are studied here. Examples are given to show that minimum aberration designs are indeed highly efficient.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssb:v:61:y:1999:i:1:p:85-93
    DOI: 10.1111/1467-9868.00164
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Zhiming Li & Zhidong Teng & Tianfang Zhang & Runchu Zhang, 2016. "Analysis on $$s^{n-m}$$ s n - m designs with general minimum lower-order confounding," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(2), pages 207-222, April.
    5. 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.
    6. 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.
    7. 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.
    8. 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).
    9. 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.
    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. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.

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