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Optimal main effect plans with non-orthogonal blocking

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  • Rahul Mukerjee

Abstract

The current literature on fractional factorial plans in block designs centres around orthogonal blocking which may not, however, always be attainable because of practical restrictions on the block size. For general factorials, including asymmetric ones, sufficient conditions are indicated in this paper for a main effect plan to be universally optimal under possibly non-orthogonal blocking. A construction procedure is given using generalised Youden designs in conjunction with orthogonal arrays. We also illustrate how the procedure can be applied to obtain optimal main effect plans in the practically important situation where each factor has two or three levels and the block size is small. Copyright Biometrika Trust 2002, Oxford University Press.

Suggested Citation

  • Rahul Mukerjee, 2002. "Optimal main effect plans with non-orthogonal blocking," Biometrika, Biometrika Trust, vol. 89(1), pages 225-229, March.
    • Handle: RePEc:oup:biomet:v:89:y:2002:i:1:p:225-229
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    Citations

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    Cited by:

    1. Jacroux, Mike & Kealy-Dichone, Bonni, 2015. "On the type I optimality of blocked 2-level main effects plans having blocks of different sizes," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 39-43.
    2. Bagchi, Sunanda & Bose, Mausumi, 2008. "Optimal main effect plans in nested row-column set-up of small size," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2720-2724, November.
    3. Bose, Mausumi & Bagchi, Sunanda, 2007. "Optimal main effect plans in blocks of small size," Statistics & Probability Letters, Elsevier, vol. 77(2), pages 142-147, January.
    4. Dutta, Ganesh & SahaRay, Rita, 2015. "D- and E-optimal blocked main effects plans with unequal block sizes when n is odd," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 37-43.
    5. Jacroux, Mike & Kealy-Dichone, Bonni, 2015. "On the use of blocked 2-level main effects plans having blocks of different sizes," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 362-368.
    6. Chen, Xue-Ping & Lin, Jin-Guan & Yang, Jian-Feng & Wang, Hong-Xia, 2015. "Construction of main-effect plans orthogonal through the block factor," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 58-64.
    7. Jacroux, Mike, 2013. "A note on the optimality of 2-level main effects plans in blocks of odd size," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1163-1166.

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