Screening experiments using supersaturated designs with application to industry

Abstract

This thesis describes the statistical methodology behind a variety of industrial screening experiments. The primary focus of the thesis is on supersaturated designs that have more parameters to be investigated than runs available. Such designs are particularly useful when experiments are expensive to perform. In addition, the statistical issues behind a real-life screening experiment are investigated, where there is a functional response and the factor levels cannot be set directly. A study to compare several existing design and analysis methods for two-level supersaturated designs was carried out. A variety of different scenarios in terms of numbers of runs, numbers of factors and numbers of active factors were investigated via simulated experiments. The Gauss-Dantzig selector was identified as an effective analysis method, whilst little difference was found in the practical performance of designs from the different criteria. As a result of the study, several guidelines are provided, to indicate when supersaturated designs are most likely to be effective as a screening tool. A new criterion for designing supersaturated experiments under measures of multicollinearity is presented. The criterion is particularly applicable to experiments where factor levels cannot be set independently, although its application to two-level designs is also demonstrated. An optimal allocation of factors to columns of an existing design is also considered.
Supersaturated experiments are discussed in the context of robust product design, where the interactions between control factors and noise factors are explored. A new criterion specifically applicable to supersaturated robust product design experiments is described. The fact that the experimenter is interested in some parameters more than others is exploited and the cost savings from using a supersaturated experiment are illustrated. It is demonstrated that substantial gains in power to detect active effects can be achieved when using this new criterion. Finally, the design and analysis of a practical screening experiment is discussed. Complicating features of the experiment include the multivariate nature of the response and the fact that factor levels cannot be set directly. A two-stage linear mixed effect model is applied, with principal components analysis used for the first stage models. A novel method for finding follow-up runs to the screening experiment is described and implemented

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ORCID for D.C. Woods: orcid.org/0000-0001-7648-429X

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