Two-stage group screening

Abstract

The work in this thesis focuses on product improvement experiments in which the response or product performance can depend on the levels of a number of different factors.  Factorial experiments are used which allow the joint effects of the different factors to be investigated and thus provide valuable information on possible interactions between the factors.  As the number of factors to be investigated increases, the number of observations needed for such an experiment can rapidly become economically infeasible.  One approach which aims to achieve a practical number of runs is to group factors together.  New grouped factors are defined to represent each group and these grouped factors are investigated in a first stage experiment.  The individual factors within those groups found to be important in the first stage experiment are then investigated in a second stage experiment.

This thesis presents new theory for this group screening approach in which the group sizes are unequal and individual control main effects, noise main effects, control x noise interactions and control x control interactions are assumed to be active with possibly different probabilities.  Examples are presented which demonstrate the investigation of different grouping strategies and group sizes through an examination of their impact on the distribution of the predicted number of effects that require estimation in the two-stage experiment.

This theory has been used in the planning of a two-stage group screening experiment at Jaguar Cars whose aim is to identify the key or active factors that influence engine cold start performance.  The experiment is described and the results are presented.

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