Multiresponse optimization of products with functional quality characteristics

In multiresponse experiments (MREs) the same experimental unit is evaluated with respect to more than one response simultaneously. Optimization of MREs typically involves determining the point in the design region where responses perform best with respect to given criteria. Utility functions are used to transform response outcomes at each experimental treatment into performance measures. Here we investigate the optimization of MREs where some response outcomes are profiles rather than individual values. A functional response gives one or more profiles as observed outcomes at each treatment, and the objective is to identify the outcome that is closest to a target profile. We propose the use of the Hausdorff distance, a similarity metric from the field of image recognition, in combination with a desirability function to obtain a utility function that gives the distance of a functional response outcome to its desired target. A case example from the food industry illustrates our propositions.