Abstract
If experimental units are inhomogeneous, before running an experiment choosing a good blocked design is the first step. Traditionally, nearly all the literature use a single block variable to treat the inhomogeneity for simplicity (see Bisggard, 1994; Wu and Hamada, 2000). However, in practice the inhomogeneity often comes from multi block variables. Therefore, for this case how to optimally choose blocking for fractional factorial designs becomes an important issue. In this paper, the ideas of AENP and GMC criterion (Zhang et al., 2008) are extended to the case of blocked regular 2n-m designs with multi block variables. By transforming the blocked aliased effect-number pattern with the case of a single block variable (denoted by B1-AENP in Zhang, Wei and Li (2009)) to the case of multi block variables (denoted by B2-AENP), we propose a criterion for choosing optimal blocked designs with this case, called B2-GMC criterion. Some theoretic results are obtained. A comparison of the B2-GMC criterion with B1-GMC and four MA-type criteria is given, and the B2-GMC, B1-GMC and the four MA-type optimal blocked designs with 16-, 32- and 64-run are tabulated.
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Zhang, R., Li, P. & Wei, J. Optimal Two-Level Regular Designs with Multi Block Variables. J Stat Theory Pract 5, 161–178 (2011). https://doi.org/10.1080/15598608.2011.10412058
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DOI: https://doi.org/10.1080/15598608.2011.10412058