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This paper introduces the generalized wordtype pattern of a nonregular fractional factorial design and considers its connection with the distance distribution. Based on the corresponding relationship between a fractional factorial design and a code, we develop a consulting design theory for fractional factorial designs with two groups of factors. It works for regular and nonregular designs and covers...
By considering the so-called algebraic orthogonality among experimental runs, this paper introduces a new criterion, minimum inner-product moment (MIPM), for general asymmetrical designs, and shows that MIPM is equivalent to the minimum moment aberration (MMA) criterion for the natural weights. Furthermore, the relationship between the generalized minimum aberration (GMA) and some model-dependent...
. Recently, Xu and Wu (2001) presented generalized minimum aberration criterion for comparing and selecting general fractional factorial designs. This criterion is defined using a set of χu(D) values, called J-characteristics by us. In this paper, we find a set of linear equations that relate the set of design points to that of J-characteristics, which implies that a factorial design is uniquely...
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