A robust optimum response surface methodology based on MM-estimator

  • Authors:

  • Habshah Midi;Mohd Shafie Mustafa;Anwar Fitrianto

  • Affiliations:

  • Department of Mathematics, Faculty Science, University Putra Malaysia, Selangor, Malaysia and Laboratory of Applied and Computational Statistics, Institute for Mathematical Research, University Pu ...;Department of Mathematics, Faculty Science, University Putra Malaysia, Selangor, Malaysia and Laboratory of Applied and Computational Statistics, Institute for Mathematical Research, University Pu ...;Department of Mathematics, Faculty Science, University Putra Malaysia, Selangor, Malaysia and Laboratory of Applied and Computational Statistics, Institute for Mathematical Research, University Pu ...

  • Venue:
  • ACS'11 Proceedings of the 11th WSEAS international conference on Applied computer science
  • Year:
  • 2011

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Abstract

A second-order polynomial model is used to fit a response surface model (RSM) whereby a facecentered composite design of experiment is considered. The parameters of the model are often estimated using the Ordinary Least Squares (OLS) method. However, the OLS method is easily affected by outliers. In this respect, 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 the optimum response. A numerical example is presented to assess the performance of the optimum response-MM based, denoted as Optimum-MM. The numerical results indicate that the Optimum-MM estimator is more efficient than the Optimum-OLS.