An Experiment to Compare Taguchi's Product Array and the Combined Array

Abstract

In robust parameter design, experimenters try to optimize a process by moving the mean to the target value and simultaneously reducing the variance. Factors that influence the mean and factors that influence the variance are determined in a designed experiment. For this experiment, Taguchi (see, e.g., Taguchi and Wu (1985)) proposed the use of a product array, where, for each combination of the design factors, the same array of noise factors is run. To identify effects on the variance, he proposed analyzing summary statistics based on the means and the variances of the response over the noise array. As an alternative, statisticians (see, e.g., Shoemaker, Tsui, and Wu (1991)) propose using a combined array of design and noise factors and analyzing the interactions between both kinds of factors. We have run an experiment (as part of a joint research project between mechanical engineers and statisticians) where we have done both designs simultaneously. In our experiment, the product array found an effect on the variance that cannot be seen from the combined array. An explanation for this might be that, at least in our example, the effect on the variance cannot be attributed to just a small number of low-order interactions.