Generalized resolution and minimum aberration criteria for plackett-burman and other nonregular factorial designs
Citations
73 citations
Cites background or methods from "Generalized resolution and minimum ..."
...To define these two important concepts, generalized resolution and generalized minimum aberration, Deng and Tang (1999) and Tang and Deng (1999) introduced the important notion of J-characteristics and is defined as follows....
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...Deng and Tang (1999) and Tang and Deng (1999) introduced the concepts of generalized resolution and generalized minimum aberration for two-level nonregular designs....
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...If δ > 0, a subset s of D with r columns contains at least Nδ/2r copies of a full 2r factorial and therefore the projectivity of D is at least r (Deng and Tang (1999))....
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...Two regular designs of the same resolution can be distinguished using the minimum aberration criterion, and the same idea can be applied to nonregular designs using the minimum G-aberration criterion (Deng and Tang (1999))....
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...Deng and Tang (1999) provided a statistical justification for the generalized resolution by showing that designs with maximum generalized resolution minimize the contamination of nonnegligible two-factor interactions on the estimation of main effects....
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71 citations
Cites background from "Generalized resolution and minimum ..."
...S)-criterion (Eccleston and Hedayat (1974)), which has long been advocated in the optimal design literature as a good surrogate for such traditional optimality criteria as the D- and A-criteria....
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...Under the hierarchical assumption that lowerorder effects are more important than higher-order effects and that effects of the same order are equally important, a minimum aberration (MA) design is preferred (Fries and Hunter (1980))....
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...Deng and Tang (1999) proposed a generalized minimum aberration criterion, a natural extension of MA from regular to nonregular designs....
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References
697 citations
"Generalized resolution and minimum ..." refers result in this paper
...Finally, we note that our argument for minimizing biases is similar to that in Box and Draper (1959)....
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471 citations
"Generalized resolution and minimum ..." refers methods in this paper
...For a detailed discussion on the concept of resolution for regular factorials, we refer to Box and Hunter (1961)....
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420 citations
"Generalized resolution and minimum ..." refers methods in this paper
...For results on minimum aberration designs, we refer to Fries and Hunter (1980), Franklin (1984), Chen and Wu (1991), Chen (1992), Tang and Wu (1996), Chen and Hedayat (1996) and Cheng, Steinberg and Sun (1999)....
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