Selection and Screening Procedures to Determine Optimal Product Designs. (REVISED, April 1997)

To compare several promising product designs manufacturers must measure their performance under multiple environmental conditions In many applications a product design is considered to be seriously awed if its performance is poor for any level of the environmental factor For example if a particular automobile battery design does not function well under temperature extremes then a manufacturer may not want to put this design into production Thus this paper considers the measure of a product s quality to be its worst performance over the levels of the environmental factor We develop statistical procedures to identify a near optimal product design among a given set of product designs i e the manufacturing design that maximizes the worst product performance over the levels of the environmental variable We accomplish this for intuitive procedures based on the split plot experimental design and the randomized complete block design as a special case split plot designs have the essential structure of a product array and the practical convenience of local randomization Two classes of statistical procedures are provided In the rst the best formulation of selection problems we determine the number of replications of the basic split plot design that are needed to guarantee with a given con dence level the selection of a product design whose minimum performance is within a speci ed amount of the performance of the optimal product design In particular if the di erence between the quality of the best and nd best manufacturing designs is or more then the procedure guarantees that the best design will be selected with speci ed probability For applications where a split plot experiment that involves several product designs has been completed without the planning required of the best formulation we provide procedures to construct a con dence subset of the manufacturing designs the selected subset contains the optimal product design with a prespeci ed con dence level The latter is called the subset selection formulation of selection problems Examples are provided to illustrate the procedures