Journal ArticleDOI
A catalogue of two-level and three-level fractional factorial designs with small runs
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TLDR
In this paper, the algebraic structure of fractional factorial (FF) designs with minimum aberration is explored and an algorithm for constructing complete sets of FF designs is proposed.Abstract:
Summary Fractional factorial (FF) designs with minimum aberration are often regarded as the best designs and are commonly used in practice. There are, however, situations in which other designs can meet practical needs better. A catalogue of designs would make it easy to search for 'best' designs according to various criteria. By exploring the algebraic structure of the FF designs, we propose an algorithm for constructing complete sets of FF designs. A collection of FF designs with 16, 27, 32 and 64 runs is given.read more
Citations
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Journal ArticleDOI
2 m 4 1 designs with minimum aberration or weak minimum aberration
TL;DR: In this paper, Wu and Zhang (1993), Zhang and Shao (2001), and Mukerjee and Wu (2001) proposed the minimum aberration (MA) criterion for measuring the goodness of 2� m�� m�� 41 designs.
Journal ArticleDOI
Design selection for strong orthogonal arrays
Chenlu Shi,Boxin Tang +1 more
TL;DR: In this article, the problem of design selection for strong orthogonal arrays (SOAs) of strength 2+ was addressed by examining their three-dimensional projections, and theoretical and computational results were presented.
Dissertation
Factorial and fractional factorial designs with randomization restrictions - a projective geometric approach
Abstract: Two-level factorial and fract,ional factsot-id designs have playcd a prominent role in the theory and pract,ice of experimental design. Though commonly used in indust.ria1 experiments to identify the significant effects, it is often undesimble to perform t,he trials of a. factorial design (or, fractional factorial design) in a complet,ely random order. Instmead, restrictions are imposed on tJhe randomization of experirne~it~al runs. In recent years, considerable attentlion has been devot,ed to fact(oria1 and fractional fa~t~orial plans with different randomization restrict,ions (e.g., nested designs, split,-plot designs, split-split-plot designs, strip-plot designs, split-lot designs, and combinatiorls thereof). Bingham et al. (2006) proposed an approach to represent. t,he randomization structlure of factorial designs with randomization restri~t~ions. This thesis introduces a related, but more general, rcpresent,ation referred to as randomization defining contrast subspaces (RDCSS). The RDCSS is a projective geometric f~rmulat~ion of mndomization defining contrast subg~oups (RDCSG) defined in Bingham et al. (2006) and allows for t,heoretical st,udy. For factorial designs with different randomization struckures, the mere existence of a design is not straightforward. Here, the t'heoretical results are developed for the existence of fact,orial designs wit,h randomization restrictions within this unified framework. Our theory brings t,ogether results from finite projective geomet,ry to establish the existence and construction of such designs. Specifically, for the existence of a set of disjoint, RDCSSs, several results are proposed using ( t 1)-spreads and partial (t 1)-spreads of PG(pI , ? ) . Furthermore, t'he t'heory developed here offers a sy~t~emat~ic approach for the const,ructtion of t,wo-level full factorial designs and regular fractional factsorial designs with randomization restrictions. Finally, when t,he ~ondit~ions for the existmeme of a set of disjoint RDCSSs are violated, the data analysis is highly influenced fro111 the overlapping pat,tern among the RDCSSs. Under t,hese circumstances, a geometric structure called star is proposed for a set of (t 1)-dimensional subspaces of PG(p 1, q) , wherc 1 < t < p. This c~periment~al p an permits the assessment of a relatively larger nnmber of fact,orial effects. The necessary and sufficient conditions for the exist,ence of stars and a collection of stars are d so developed here. In particular, stars ~onsti t~ute useful designs for practitioners because of their flexith structure and easy construction.
Journal ArticleDOI
Robust designs through partially clear two-factor interactions
Ryan Lekivetz,Boxin Tang +1 more
TL;DR: In this paper, the existence and construction of robust orthogonal arrays with clear two-factor interactions was studied and an upper bound on the maximum number of clear two factor interactions was presented.
Issues in applying statistical design of experiments, with special reference to toxicology of mixtures
TL;DR: The final author version and the galley proof are versions of the publication after peer review and the final published version features the final layout of the paper including the volume, issue and page numbers.
References
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Journal ArticleDOI
Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building.
Journal ArticleDOI
The 2 k-p fractional factorial designs part I
George E. P. Box,J. S. Hunter +1 more
TL;DR: The 2 k-p Fractional Factorial Designs Part I. as discussed by the authors is a collection of fractional fractional factorial designs with a focus on the construction of the construction.
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.