Construction of supersaturated split-plot designs
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Construction of supersaturated split-plot designs K. Chatterjee1 · C. Koukouvinos2
· K. Mylona3,4
Received: 14 December 2017 / Revised: 8 August 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract We propose a combinatorial construction method for setting up informative experiments with both restricted randomisation and a large number of factors. The supersaturated split-plot designs are very useful in screening situations where the number of factors is larger than the number of available observations and several of these factors have levels that they are hard to change. The construction method is based on compound orthogonal arrays. We evaluate the constructed designs using an optimality criterion and we provide a lower bound for this criterion. Keywords Compound orthogonal array · Supersaturated split-plot design · Optimality · Lower bound
1 Introduction In quantitative work in any field of application, data collection issues are at least as important as data analysis. Haphazard experimentation can be very wasteful of resources [for an overview in design of experiments, see Draper and Pukelsheim (1996) and Dean et al. (2015)]. The supersaturated split-plot designs (SSSPDs) combine two very important classes of designs for screening situations. Firstly, the supersaturated designs (SSDs) is a large class of factorial designs which can be used for screening out the important factors from a large set of potentially active variables. They are designs with m factors and n observations, where n ≤ m. In Georgiou (2014), an extensive literature review on the constructions and analysis methods of supersaturated designs is provided. Supersaturated experiments are usually designed assuming the treatments
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C. Koukouvinos [email protected]
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Department of Statistics, Visva-Bharati University, Santiniketan, West Bengal, India
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Department of Mathematics, National Technical University of Athens, 15773 Zografou, Athens, Greece
3
Department of Mathematics, King’s College London, Strand, London WC2R 2LS, UK
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Department of Statistics, University Carlos III de Madrid, Calle Madrid 126, Getafe, Spain
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(combinations of factor levels) are completely randomised to the experimental units. However, just as with any designed experiment, there may be some structure in the experimental units; for example, if the units are sequential runs some factors may have to be changed less frequently than every run (e.g. factors whose levels are hard or costly to change). The split-plot designs are very effective in reducing the cost of an experiment in the presence of hard-to-change factors and/or of two-stage processes. There is a large body of published research on split-plot designs (e.g., Goos 2002; Aastveit et al. 2009; Jones and Nachtsheim 2009). Specifically, a significant amount of research focuses on fractional factorial split-plot designs. These designs are constructed by using regular or non-regular fractional factorial designs at the two-stage randomisation. Examples of c
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