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Optimal two-level regular fractional factorial block and split-plot designs
Department of Statistics, University of California, Berkeley, California 94720, U.S.A. cheng{at}stat.berkeley.edu
Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan pwtsai{at}math.ntnu.edu.tw
Received for publication 1 August 2007. Revision received 1 June 2008.
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.
Key Words: Alias set • Estimation capacity • Information capacity • Minimum aberration • Model robustness • Word length pattern
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