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Optimal two-level regular fractional factorial block and split-plot designs

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  • Ching-Shui Cheng
  • Pi-Wen Tsai

Abstract

We propose a general and unified approach to the selection of regular fractional factorial designs, which can be applied to experiments that are unblocked, blocked or have a split-plot structure. Our criterion is derived as a good surrogate for the model-robustness criterion of information capacity. In the case of random block effects, it takes the ratio of intra- and interblock variances into account. In most of the cases we have examined, there exist designs that are optimal for all values of that ratio. Examples of optimal designs that depend on the ratio are provided. We also demonstrate that our criterion can further discriminate designs that cannot be distinguished by the existing minimum-aberration criteria. Copyright 2009, Oxford University Press.

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  • Ching-Shui Cheng & Pi-Wen Tsai, 2009. "Optimal two-level regular fractional factorial block and split-plot designs," Biometrika, Biometrika Trust, vol. 96(1), pages 83-93.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:1:p:83-93
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    File URL: http://hdl.handle.net/10.1093/biomet/asn066
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    Cited by:

    1. T. I. Katsaounis, 2022. "On multistage experiments with restrictions in the randomization of treatments," Statistical Papers, Springer, vol. 63(2), pages 531-541, April.
    2. Steven G. Gilmour & Peter Goos, 2009. "Analysis of data from non‐orthogonal multistratum designs in industrial experiments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(4), pages 467-484, September.
    3. Wang, Xiaodi & Chen, Xueping & Zhang, Yingshan, 2018. "Feasible blocked multi-factor designs of unequal block sizes," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 102-109.

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