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Statistica Sinica 18(2008), 1689-1705





A GENERAL MINIMUM LOWER-ORDER CONFOUNDING

CRITERION FOR TWO-LEVEL REGULAR DESIGNS


Runchu Zhang$^{1,2}$, Peng Li$^{1}$, Shengli Zhao$^{1,3}$ and Mingyao Ai$^{4}$


$^1$Nankai University, $^2$Northeast Normal University,
$^3$Qufu Normal University and $^4$Peking University
Abstract: Based on the effect hierarchy principle in experimental design, an aliased effect-number pattern (AENP, or AP for short) is proposed to judge two-level regular designs; it contains the basic information of all effects aliased with other effects at varying severity degrees in a design. Based on the AENP, a general minimum lower-order confounding (GMLOC, or GMC for short) criterion is proposed, and several results follow. First, the word-length pattern, as the core of the minimum aberration (MA) criterion, is a function of the AENP. The same also holds for the clear effects (CE) criterion. Furthermore, the estimation capacity (EC) of a design can be also calculated as a function of the new pattern, and links between the MA and CE criteria are discovered. In addition, a concept of estimation ability is introduced, and it is concluded that a GMC design is the one with the best estimation ability. Finally, more applications of the new pattern are given. All GMC designs of 16 and 32 runs, a number of GMC designs of 64 runs, and some comparisons with the optimal designs under MA and CE criteria are tabulated.



Key words and phrases: Clear effects criterion, effect hierarchy principle, estimation ability, estimation capacity, minimum aberration.

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