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Statistica Sinica 20 (2010), 183-207





OPTIMAL BLOCKING AND FOLDOVER PLANS FOR

REGULAR TWO-LEVEL DESIGNS


Mingyao Ai$^{1}$, Xu Xu$^{1}$ and C. F. Jeff Wu$^{2}$


$^1$Peking University and $^2$Georgia Institute of Technology


Abstract: This article considers the problem of choosing optimal designs when both blocking and foldover techniques are employed. Based on a general decomposition structure, the treatment and block split wordlength patterns of the combined blocked design under a general foldover plan are defined. They are proved to be independent of the choice of the block foldover plans. It is shown that, for an initial unblocked design, a pair of blocking and foldover plans has minimum aberration for the combined blocked design if and only if the foldover plan has minimum aberration without consideration of blocking plans and the blocking plan has minimum aberration without consideration of foldover plans. The clear effects in the combined blocked designs are also characterized. Based on these theoretical results, a catalogue of optimal blocking and foldover plans in terms of the aberration and clear effect criteria is tabulated.



Key words and phrases: Clear effect, minimum aberration, split wordlength pattern.

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