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Journal ArticleDOI

Minimum Aberration 2 k–p Designs

01 Nov 1980-Technometrics (Taylor & Francis Group)-Vol. 22, Iss: 4, pp 601-608
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.
Citations
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Journal ArticleDOI
01 Sep 2007
TL;DR: In this article, the authors give some linkages between uniformity measured by the discrete discrepancy and other criteria, such as generalized minimum aberration and minimum projection variance, and provide an additional rationale for using uniform designs.
Abstract: Discrete discrepancy has been utilized as a uniformity measure for comparing and evaluating factorial designs. In this paper, for asymmetrical factorials, we give some linkages between uniformity measured by the discrete discrepancy and other criteria, such as generalized minimum aberration (Xu and Wu, 2001) and minimum projection variance (Ai and Zhang, 2004). These close linkages show a significant justification for the discrete discrepancy used to measure uniformity of factorial designs, and provide an additional rationale for using uniform designs.

16 citations

Journal ArticleDOI
01 Jul 2008
TL;DR: In this article, the existence of clear 2fic's in regular 2m4n designs with resolution III or IV has been studied and the necessary and sufficient conditions for a 2m 4n design to have clear two-factor interaction components are given.
Abstract: The orthogonal arrays with mixed levels have become widely used in fractional factorial designs. It is highly desirable to know when such designs with resolution III or IV have clear two-factor interaction components (2fic’s). In this paper, we give a complete classification of the existence of clear 2fic’s in regular 2m4n designs with resolution III or IV. The necessary and sufficient conditions for a 2m4n design to have clear 2fic’s are given. Also, 2m4n designs of 32 runs with the most clear 2fic’s are given for n = 1,2.

16 citations


Cites background from "Minimum Aberration 2 k–p Designs"

  • ...Under such circumstances, minimum aberration (Fries and Hunter 1980) is the most often used criterion for selecting good designs....

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Journal ArticleDOI
TL;DR: This work considers the problem of selecting two-level fractional factorial designs that allow joint estimation of all main effects and some specified two-factor interactions (2fi’s) without aliasing from other 2fi”s, and calls a 2 m−p resolution IV design admissible if its graph is not isomorphic to any proper subgraph of the graph of any other 2m−presolution IV design.
Abstract: We consider the problem of selecting two-level fractional factorial designs that allow joint estimation of all main effects and some specified two-factor interactions (2fi’s) without aliasing from other 2fi’s. This problem is to find, among all 2 m−p designs with given m and p, those resolution IV designs whose sets of clear 2fi’s contain the specified 2fi’s as subsets. We use a linear graph to represent the set of clear 2fi’s for a resolution IV design, where each line connecting two vertexes represents a clear 2fi between the factors represented by the two vertexes. We call a 2 m−p resolution IV design admissible if its graph is not isomorphic to any proper subgraph of the graph of any other 2 m−p resolution IV design. We show that all even resolution IV designs are inadmissible. We then use a classical subgraph-isomorphism algorithm to determine all admissible designs of 32, 64, and 128 runs. This leads to a concise catalog of all admissible designs of 32 and 64 runs, and a lengthy but substantially re...

16 citations


Cites background from "Minimum Aberration 2 k–p Designs"

  • ...If there is no design with less aberration than d1, d1 has MA (Fries and Hunter 1980)....

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  • ...Of special importance in this connection are minimum aberration (MA) designs (Fries and Hunter 1980), designs with the maximum number of clear 2fi’s (MaxC2 designs) (Wu and Wu 2002), Bayesian D-optimal designs (DuMouchel and Jones 1994), and D-efficient minimal aliasing designs (Jones and…...

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  • ...On the other hand, MA designs (Fries and Hunter 1980) and weak MA designs (Chen and Hedayat 1996) are generally admissible for m slightly larger than M(k) and inadmissible for larger m....

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  • ...Of special importance in this connection are minimum aberration (MA) designs (Fries and Hunter 1980 ), designs with the maximum number of clear 2fi’s (MaxC2 designs) (Wu and Wu 2002 ), Bayesian D-optimal designs (DuMouchel and Jones 1994 ), and D-efficient minimal aliasing designs (Jones and Nachtsheim 2011 )....

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Journal ArticleDOI
TL;DR: In this paper, the first term of the wordlengh pattern of regular 2n−m designs has been shown to be the optimal confounding structure for two-level regular designs.

16 citations

Journal ArticleDOI
TL;DR: In this paper, a word-length pattern for non-regular fractional factorial designs with two different types of factors is proposed to rank robust parameter designs and the authors show that one can easily find minimum aberration robust parameters from existing orthogonal arrays.

15 citations

References
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Book
01 Jan 1978

5,151 citations

Book
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

Journal ArticleDOI
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