Screening Procedures to Identify Robust Product or Process Designs Using Fractional Factorial Experiments

In many quality improvement experiments, there are one or more ``control'' factors that can be modified to determine a final product design or manufacturing process, and one or more ``environmental'' (or `` noise'') factors that vary under field or manufacturing conditions. In many applications, the product design or process design is considered seriously flawed if its performance is poor for any level of the environmental factor. For example, if a particular prosthetic heart valve design has poor fluid flow characteristics for certain flow rates, then a manufacturer will not want to put this design into production. Thus this paper considers cases when it is appropriate to measure a product's quality to be its {\em worst} performance over the levels of the environmental factor. We consider the frequently occurring case of combined-array experiments and extend the subset selection methodology of Gupta (1956, 1965) to provide statistical screening procedures to identify product designs that maximize the worst case performance of the design over the environmental conditions for such experiments. A case study is provided to illustrate the proposed procedures