The Use of Subset Selection in Combined Array Experiments to Determine Optimal Product or Process Designs. (REVISED, June 1997)

A number of authors in the quality control literature have
advocated the use of combined-arrays in screening experiments to
identify robust product or process designs [Shoemaker, Tsui, and Wu
(1991); Nair et al. (1992); Myers, Khuri, and Vining (1992), for
example]. This paper considers a product manufacturing or process
design setting in which there are several factors under the control
of the manufacturer, called control settings, and other
environmental (noise) factors that that vary under field or
manufacturing conditions. We show how Gupta's subset selection
philosophy can be used in such a quality improvement setting to
identify combinations of the levels of the control factors that
correspond either to products that are robust to environmental
variations during their use or to processes that fabricate items
whose quality is independent of the variations in the raw materials
used in their manufacture. [Gupta (1956, 1965)].