Minimum Aberration 2 k–p Designs
TL;DR: In this article, the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution, and algorithms are presented for constructing these minimum aberration designs.
Abstract: For studying k variables in N runs, all 2 k–p designs of maximum resolution are not equally good. In this paper the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution. Algorithms are presented for constructing these minimum aberration designs.
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TL;DR: In this paper, a systematic construction for 1/8th and 1/16th fraction quaternary codes with high resolution for any number of factors is presented, and a majority of these designs have larger resolution than comparable two-level regular designs.
8 citations
TL;DR: Li et al. as mentioned in this paper constructed all the GMC designs with N/4+1/le n/le N-1, where n is the run number and n is factor number.
Abstract: Zhang et al. (Stat Sinica 18:1689–1705, 2008) introduced an aliased effect-number pattern for two-level regular designs and proposed a general minimum lower-order confounding (GMC) criterion for choosing optimal designs. All the GMC \(2^{n-m}\) designs with \(N/4+1\le n\le N-1\) were constructed by Li et al. (Stat Sinica 21:1571–1589, 2011), Zhang and Cheng (J Stat Plan Inference 140:1719–1730, 2010) and Cheng and Zhang (J Stat Plan Inference 140:2384–2394, 2010), where \(N=2^{n-m}\) is run number and \(n\) is factor number. In this paper, we first study some further properties of GMC design, then we construct all the GMC \(2^{n-m}\) designs respectively with the three parameter cases of \(n\le N-1\): (i) \(m\le 4\), (ii) \(m\ge 5\) and \(n=(2^m-1)u+r\) for \(u>0\) and \(r=0,1,2\), and (iii) \(m\ge 5\) and \(n=(2^m-1)u+r\) for \(u\ge 0\) and \(r=2^m-3,2^m-2\).
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TL;DR: The foldover plan as discussed by the authors is a transformation map for adding a foldover design to the initial design, thus resulting in a combined design which can be used for breaking the links between aliased ef...
Abstract: The foldover plan is a transformation map for adding a foldover design to the initial design, thus resulting in a combined design which can be used for breaking the links between aliased ef...
8 citations
TL;DR: In this paper, the authors extend GMC theory to s-level regular designs, where s is a prime or prime power, and obtain three necessary conditions for design D to have GMC.
Abstract: An optimal design should minimize the confounding among factor effects, especially the lower-order effects, such as main effects and two-factor interaction effects. Based on the aliased component-number pattern, general minimum lower-order confounding (GMC) criterion can provide the confounding information among factors of designs in a more elaborate and explicit manner. In this paper, we extend GMC theory to s-level regular designs, where s is a prime or prime power. For an \(s^{n-m}\) design D with \(N=s^{n-m}\) runs, the confounding of design D is given by complementary set. Further, according to the factor number n, we discuss two cases: (i) \(N/s
8 citations
TL;DR: In this paper, a general method for finding optimal blocking arrangements of pure-level and mixed-level orthogonal designs of resolution 3 was presented, which requires enumeration of all nonisomorphic "full designs" that include the treatment factors as well as the blocking factor.
Abstract: This paper presents a general method for finding optimal blocking arrangements of pure-level and mixed-level orthogonal designs of resolution 3. The method requires enumeration of all nonisomorphic 'full designs' that include the treatment factors as well as the blocking factor. For all these designs, generalized word counts expressing the aliasing between main effects and two-factor interactions as well as the aliasing among two-factor interactions are calculated. The same is done for all projections into treatment designs obtained by dropping any possible blocking factor. The generalized word counts of the full design and treatment designs then allow the selection of blocking arrangements that are optimal with respect to five criteria appropriate for blocking resolution-3 orthogonal designs. We provide optimal blocking arrangements for orthogonal pure-level and mixed-level designs of 12, 16, 18, 20, and 27 runs.
8 citations
Cites background from "Minimum Aberration 2 k–p Designs"
...…equal resolution, Xu and Wu (2001) use a generalized aberration (GA) criterion similar to the aberration criterion for regular fractional factorial two-level designs (Fries and Hunter (1980)) and the G2 aberration criterion for both regular and nonregular two-level designs (Tang and Deng (1999))....
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References
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471 citations
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23 Jun 1976
TL;DR: In conclusion, the size of Industrial Experiments, Fractional Replication--Elementary, and Incomplete Factorials are found to be about the same as that of conventional comparison experiments.
Abstract: Introduction. Simple Comparison Experiments. Two Factors, Each at Two Levels. Two Factors, Each at Three Levels. Unreplicated Three--Factor, Two--Level Experiments. Unreplicated Four--Factor, Two--Level Experiments. Three Five--Factor, Two--Level Unreplicated Experiments. Larger Two--Way Layouts. The Size of Industrial Experiments. Blocking Factorial Experiments, Fractional Replication--Elementary. Fractional Replication--Intermediate. Incomplete Factorials. Sequences of Fractional Replicates. Trend--Robust Plans. Nested Designs. Conclusions and Apologies.
311 citations
09 Jun 1976
271 citations
TL;DR: Incomplete Factorials, Fractional Replication, Intermediate Factorial, and Nested Designs as discussed by the authors are some of the examples of incomplete Factorial Experiments and incomplete fractional replicates.
Abstract: Introduction. Simple Comparison Experiments. Two Factors, Each at Two Levels. Two Factors, Each at Three Levels. Unreplicated Three--Factor, Two--Level Experiments. Unreplicated Four--Factor, Two--Level Experiments. Three Five--Factor, Two--Level Unreplicated Experiments. Larger Two--Way Layouts. The Size of Industrial Experiments. Blocking Factorial Experiments, Fractional Replication--Elementary. Fractional Replication--Intermediate. Incomplete Factorials. Sequences of Fractional Replicates. Trend--Robust Plans. Nested Designs. Conclusions and Apologies.
252 citations