The MM-Estimator in Response Surface Methodology

In this article, a robust regression technique called MM-estimator is proposed to model the responses in response surface methodology (RSM). Model fitting based on the MM-estimator allows practitioners to find a better optimal setting in dual-response surface optimization and multiple-response optimization when the responses are considerably nonnormal and/or contain some outliers. The MM-estimator is one of the robust regression techniques that can dampen the effect of the outliers. An example from the Roman catapult experiment is used to illustrate our proposal.

Keywords:

• Robust regression
• MM-estimator
• Breakdown point
• Efficiency
• Optimization
• Ordinary least squares (OLS)
• Weighted least squares (WLS)
• Generalized reduced gradient (GRG)

ACKNOWLEDGMENT

The authors want to thank the referee, Professor Seyda Deligonul, for his helpful comments and suggestions, which have improved the contents and style of the article.

Additional information

Notes on contributors

C. K. Ch'ng

C. K. Ch'ng is a doctoral student in Statistics at the School of Mathematical Sciences, University of Science of Malaysia. His research interests are statistical process control and response surface methodology

S. H. Quah

S. H. Quah is a professor of statistics in the School of Mathematical Sciences, University of Science of Malaysia. His fields of interest are quality management, statistical process control, and statistical design of experiments

H. C. Low

H. C. Low is an associate professor of statistics in the School of Mathematical Sciences, University of Science of Malaysia. Her fields of interest are statistical process control, medical statistics, and signal processing