Noise Variable Settings in Robust Design Experiments

Abstract

In robust design studies, the important noise factors are varied systematically in off-line experiments and their interactions with control factors are investigated. The choice of the noise variable settings is extremely important in being able to achieve the goal of robust design studies. However, the noise distributions are rarely known, and the choices are often based on convenience. This article demonstrates some of the unintended and undesirable consequences of such choices, including identification of small dispersion effects as important, missing of large ones, and issues with parameter optimization. The main contribution of the article is to propose an alternative method of analysis for identifying important dispersion effects, one based on separate analysis for each noise factor. The method is tailored for situations with crossed-array designs. There are, however, still challenges associated with choosing the control factor settings to achieve robust performance. Further, there are difficulties with the use of combined arrays in such cases. The focus of the article is on direct modeling of the responses but implications for mean–variance analyses are also discussed.

KEY WORDS:

• Control-by-noise interactions
• Location-dispersion analysis
• Noise factors
• Parameter design
• Response-model analysis.

ACKNOWLEDGMENTS

We thank Sheela Laber and Aijun Zhang for their help with the simulations and analysis. We are grateful to the Editor, Associate Editor, and two referees for very useful comments and for additional references. Bingham’s research was supported by the Natural Science and Engineering Research Council of Canada. Nair’s research was partially supported by a National Institutes of Health (NIH) grant.