Identifying Dispersion Effects in Robust Design Experiments—Issues and Improvements

The two experimental methods most commonly used for reducing the effect of noise factors on a response of interest Y aim either to estimate a model of the variability (V(Y), or an associated function), that is transmitted by the noise factors, or to estimate a model of the ratio between the response (Y) and all the control and noise factors involved therein. Both methods aim to determine which control factor conditions minimise the noise factors' effect on the response of interest, and a series of analytical guidelines are established to reach this end. Product array designs allow robustness problems to be solved in both ways, but require a large number of experiments. Thus, practitioners tend to choose more economical designs that only allow them to model the surface response for Y. The general assumption is that both methods would lead to similar conclusions. In this article we present a case that utilises a design based on a product design and for which the conclusions yielded by the two analytical methods are quite different. This example casts doubt on the guidelines that experimental practice follows when using either of the two methods. Based on this example, we show the causes behind these discrepancies and we propose a number of guidelines to help researchers in the design and interpretation of robustness problems when using either of the two methods.