Journal ArticleDOI
On simplifying the calculations leading to designs with general minimum lower-order confounding
Jia-Lin Wei,Jian-Feng Yang +1 more
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In this paper, a simple method for the calculation of aliased effect number pattern (AENP) was proposed, which is much easier than before since the calculation only makes use of the design matrix, and all 128 run GMC designs with the number of factors ranging from 8 to 32 are provided for practical use.Abstract:
Motivated by the effect hierarchy principle, Zhang et al. (Stat Sinica 18:1689–1705, 2008) introduced an aliased effect number pattern (AENP) for regular fractional factorial designs and based on the new pattern proposed a general minimum lower-order confounding (GMC) criterion for choosing optimal $$2^{n-m}$$
designs. Zhang et al. (Stat Sinica 18:1689–1705, 2008) proved that most existing criteria can be obtained by functions of the AENP. In this paper we propose a simple method for the calculation of AENP. The method is much easier than before since the calculation only makes use of the design matrix. All 128-run GMC designs with the number of factors ranging from 8 to 32 are provided for practical use.read more
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Results on constructing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e1281" altimg="si7.svg"><mml:msup><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mi>m</mml:mi></mml:mrow></mml:msup></mml:math> regular designs with gene
TL;DR: For s-level regular designs, an aliased component effect number pattern (AENP) can be used to investigate all of confounding information among factorial component effects as discussed by the authors .
Journal ArticleDOI
Computer algorithms of lower-order confounding in regular designs
Zhi Ming Li,Zhiming Li +1 more
References
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MonographDOI
Experiments : planning, analysis, and optimization
C. F. Jeff Wu,Michael S. Hamada +1 more
TL;DR: In this article, the authors present a survey of the state-of-the-art techniques for the planning and implementation of experiments, including replication, randomization, and blocking.
Journal ArticleDOI
Minimum Aberration 2 k–p Designs
Arthur Fries,William G. Hunter +1 more
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.
Journal ArticleDOI
A graph-aided method for planning two-level experiments when certain interactions are important
Chien-Fu Wu,Youyi Chen +1 more
TL;DR: In this paper, a graph-aided method is proposed to solve the problem of fractional factorial factorial experiment planning, where prior knowledge may suggest that some interactions are potentially important and should therefore be estimated free of the main effects.
Book
A modern theory of factorial designs
Rahul Mukerjee,C. F. Jeff Wu +1 more
TL;DR: In this paper, the authors present a comprehensive and up-to-date account of optimal factorial design, under possible model uncertainty, via the minimum aberration and related criteria.
Journal ArticleDOI
Optimal Blocking Schemes for 2n and 2n—p Designs
TL;DR: In this article, the authors proposed a blocking scheme for fractional factorial experiments based on the minimum aberration criterion and a related concept of order of estimability to reduce the sources of variations in factorial tests.