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The design and analysis of experiments.
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Journal ArticleDOI
A Method of Constrained Randomization for 2 n Factorials
Kenneth J. Tiahrt,D. L. Weeks +1 more
TL;DR: In this article, the authors presented methods of constrained randomization for 2 n-p factorial experiments in blocked designs when the requirment (imposed by the nature of the process under investigation) on adjacent treatment combinations restricts the number of factor levels which may be changed from run to run (treatment combination to adjacent treatment combination).
Journal ArticleDOI
Relations between composition and viscosity of cow's milk
TL;DR: Theoretical and practical aspects of the apparent or effective viscosity of milk have been studied by many workers: see reviews by Scott Blair and others.
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
Individual control treatment in split-plot experiments
TL;DR: In this article, the control (standard) may not be strictly connected with treatment combinations, and the new incomplete split-plot designs with control satisfy all generally accepted methodological requirements, with special reference to the problems of randomisation.