Analysis of functional responses from robust design studies

Robust design studies with functional responses are becoming increasingly common. The goal in these studies is to analyze location and dispersion effects and optimize performance over a range of input-output values. Taguchi and others have proposed the so-called signal-to-noise ratio analysis for robust design with dynamic characteristics. We consider more general and flexible methods for analyzing location and dispersion effects from such studies and use three real applications to illustrate the methods. Two applications demonstrate the usefulness of functional regression techniques for location and dispersion analysis while the third illustrates a parametric analysis with two-stage modeling. Both a mean-variance analysis for random selection of noise settings as well as a control-by-noise interaction analysis for explicitly controlled noise factors are considered.