# Generalized resolution and minimum aberration criteria for plackett-burman and other nonregular factorial designs

TL;DR: In this paper, a generalized resolution criterion is defined and used for assessing non-regular fractional factorials, notably Plackett-Burman designs, which is intended to capture projection properties, complementing that of Webb (1964) whose concept of resolution concerns the estimability of lower order fractional fractional factors under the assumption that higher order effects are negligible.

Abstract: Resolution has been the most widely used criterion for comparing regular fractional factorials since it was introduced in 1961 by Box and Hunter. In this pa- per, we examine how a generalized resolution criterion can be defined and used for assessing nonregular fractional factorials, notably Plackett-Burman designs. Our generalization is intended to capture projection properties, complementing that of Webb (1964) whose concept of resolution concerns the estimability of lower order ef- fects under the assumption that higher order effects are negligible. Our generalized resolution provides a fruitful criterion for ranking different designs while Webb's resolution is mainly useful as a classification rule. An additional advantage of our approach is that the idea leads to a natural generalization of minimum aberration. Examples are given to illustrate the usefulness of the new criteria.

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##### Citations

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### Additional excerpts

...(See Lin and Draper 1992, Wang and Wu 1995, Cheng 1995, Box and Tyssedal 1996, Deng and Tang 1999, Tang and Deng 1999, and Xu and Wu 2001 for classi cation or discrimination of OAs.)...

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100 citations

### Cites background from "Generalized resolution and minimum ..."

...For orthogonal designs, Jk4s5 must be a multiple of 4 (Deng and Tang 1999, prop....

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...The minimum G-aberration criterion introduced in Deng and Tang (1999) is de ned as follows. For two designs D1 and D2, let fi4D15 and fi4D25 be the ith entries of F 4D15 and F4D25, respectively, where i D 11 : : : 1 4m ƒ 25t. Let l be the smallest integer such that fl4D15 6D fl4D25. If fl4D15 < fl4D25, then D1 has less G aberration than D2. If no design has less G aberration than D1, then D1 has minimum G aberration. Tang and Deng (1999) proposed a relaxed version of minimum G aberration, called minimum G2 aberration....

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...1 reviews the criteria of generalized minimum aberration proposed in Deng and Tang (1999) and Tang and Deng (1999)....

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...Section 2.1 reviews the criteria of generalized minimum aberration proposed in Deng and Tang (1999) and Tang and Deng (1999)....

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...…Aberration Criteria Lih-Yuan Deng and Boxin Tang Department of Mathematical Sciences University of Memphis Memphis, TN 38152 ( btang@memphis.edu ) Deng and Tang (1999) and Tang and Deng (1999) proposed and justi ed two criteria of generalized minimum aberration for general two-level fractional…...

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99 citations

### Cites background from "Generalized resolution and minimum ..."

...What should be mentioned here are the J−Characteristics used by Deng and Tang (1999) as building blocks in defining their generalized aberration criterion....

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...(Deng and Tang, 1999) Regard a n × s design as a set of s columns A = {c1, c2, · · · , cs}....

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...Recently, Deng and Tang (1999) and Tang and Deng (2000) generalize resolution and aberration criterion to nonregular two-level designs based on the J−Characteristics....

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##### References

679 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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457 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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### "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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