Christine Sexton - Department of Mathematics, University of Southampton, SO۱۷ ۱BJ, UK.
Sue Lewis - Department of Mathematics, University of Southampton, SO۱۷ ۱BJ, UK.
Colin Please - Department of Mathematics, University of Southampton, SO۱۷ ۱BJ, UK.

For experiments on mechanical products composed of several components, conventional methods of designing and implementing factorial experiments can be infeasible because of the prohibitive costs of obtaining certain components with factors set to pre-specified values. A further difficulty for many products is that some or all of the factors believed to influence the product’s performance are not features of a single component, but are derived as functions of the dimensions of two or more components arising from the product’s assembly. This paper describes how optimal design methods have enabled efficient and economic experiments involving such derived factors to be planned and performed. The approach developed uses a modest sample of measured components which are assembled into products for testing in a way that gives as much information as possible on the factorial effects of interest. Thus full control is sacrificed over the values taken by factors, but some control is retained over which factor values are combined in the experiment. An algorithm for finding optimal designs is discussed which uses an exchange procedure. The issues of correlations amongst parameter estimators and robustness of the designs to missing data are also discussed. The approach is illustrated via a study on hydraulic gear pumps from the automotive industry.