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

In his pioneering work on product and process improvement, Taguchi (1986) emphasizes two types of factors that effect product quality: “control factors” are those variables that can be (easily) manipulated by the manufacturer and “noise factors” are those variables that represent either different environmental conditions that affect the performance of a product in the field or (uncontrollable) variability in component parts or raw materials that affect the performance of an end-product. For experiments to improve product or process design, Taguchi advocates using statistical designs that are products of highly fractionated orthogonal arrays in the control and noise factors. In the case of product design, for example, the goal of such experiments is to determine conditions under which the mean product quality is independent of the noise factors. While some of Taguchi’s proposals have been controversial [Box (1988)], the basic viewpoint that he advocates has been applied widely and with many successes [Taguchi and Phadke (1984)]. A number of authors have proposed statistical refinements to the Taguchi methodology [Shoemaker, Tsui, and Wu (1991); Nair et al. (1992); Myers, Khuri, and Vining (1992), for example]. One of these proposals is to use combined-arrays in the control and noise factors to design quality improvement experiments rather than Taguchi’s product-arrays. At the expense of confounding higher-order interactions, carefully chosen combined-arrays allow the experimenter to determine interactions among the control factors and interactions among the noise factors, as well as the critical control factor by noise factor interactions that allow one to minimize the effect of noise factors in product quality. A second proposal is to apply response surface methodology to the combined-array data to identify parsimonious models for the quality character-