A New Design Criterion for Robust Parameter Experiments

Abstract

Varying noise factors in an experiment allows us to find robust conditions against such variation. The levels of the noise factors need to be selected carefully. Levels that are too wide may be infeasible or too costly, and if too narrow they may not provide a good model for prediction and control purposes. We propose a noise-factor separation (NFS) criterion for designs used in robust parameter design, in which a design is preferred to another if it provides the same expected mean square error for the noise part of the fitted model but for a smaller range of the noise factors in uncoded units. We evaluate several experimental designs that can be used to fit a response model that is quadratic in the controllable factors and also contains noise main effects and noise × control interactions. It is shown how the new criterion is related to variance dispersion graphs for the slope and may be used in conjunction with these graphs to assess a given experimental design. The new criterion is incorporated into an optimization formulation used to find new three-level designs that also includes traditional design criteria, such a D-efficiency. A Genetic algorithm was developed to solve such formulation. It is shown how the new designs are competitive in terms of design size, noise-factor separation, and variance dispersion for the mean and slope with respect to composite mixed resolution designs.