Robust analysis of a response surface design

Abstract

The paper discusses the outlier issue in experiments that are carefully planned for the purpose of response surface exploration. In such cases, a second order polynomial is fitted to the measurements in order to identify significant control variables, optimal settings of control variables, likely gains in the value of the response, etc. Outliers among the measurements cannot be avoided and will almost certainly have a highly confusing effect on the least-squares fit, leading to a wrong interpretation of the data. The paper discusses a practical example and uses it to exhibit two possible approaches. A combination of the least-squares technique with an expert knowledge of the design of the experiment can lead to valid interpretations by highlighting the trouble spots. The other possible approach uses robust fitting techniques which are much less easily fooled by outliers and automatically account for them. The second approach is better suited to casual users of response surface methodology.