The Performance of Optimum Response S urface Methodology Based on MM-Estimator

The Ordinary Least Squares (OLS) method is often used to estimate the parameters of a second-order polynomial response surface methodology (RSM) model whereby a face-centered composite design of experiment is considered. The parameters of the model are usually estimated using the OLS technique. Nevertheless, the classical OLS suffers a huge set back in the presence of a typical observations that we often call outliers. In this situation, the optimum response estimator is not reliable as it is based on the OLS which is not resistant to outliers. As an alternative, we propose using a robust MM-estimator to estimate the parameters of the RSM and subsequently the optimum response is determined. A numerical example and simulation study are presented to assess the performance of the optimum response-MM based, denoted as Optimum-MM. The numerical results signify that the Optimum-MM is more efficient than the Optimum-OLS.

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