The Use of Subset Selection in Combined-Array Experiments to Determine Optimal Product or Process Designs

Abstract

In the quality control literature, a number of authors have advocated the use of combined-arrays in screening experiments to identify robust product designs or robust process designs [Shoemaker, Tsui and Wu (1991); Nair et al. (1992); Myers, Khuri and Vining (1992), among others]. This paper considers product design and process design applications in which there are one or more “control” factors that can be modified by the manufacturer, and one or more “environmental” (or “noise”) factors that vary under field or manufacturing conditions. We show how Gupta’s subset selection philosophy can be implemented in such a setting to identify optimal combinations of the levels of the control factors [Gupta (1956, 1965)]. By optimal, we mean those settings of the control factors that yield product designs whose performance is the most robust to variations in environmental factors. For process designs, the optimal settings of the control factors yield a fabrication method whose product quality is as nearly independent as possible to variations in the uncontrollable manufacturing factors, for example, to daily temperature fluctuations.