Multivariable power least squares method: Complementary tool for Response Surface Methodology

Abstract

In Response Surface Methodology (RSM), variables are correlated through polynomial functions based on Stone-Weierstrass theorem. However, such formulation inherits four weaknesses: possible misleading approximation, incapability to accurately determine the ranking of factors' dominance, failure to analyse factors in random value and proliferation of guess functions due to Pascal Triangle. Therefore, this article aims to develop an improvised method to rectify and complement the weaknesses of RSM. Multivariable Power Least Squares Method (MPLSM) has been developed to correlate various sets of independent variables with dependent variable in the form of power functions. MPLSM is built upon least squares method, and able to approximate the indices of the variables easily. Two variants of MPLSM are suggested to further ensure the numerical stability: the Normalised MPLSM and Iterative MPLSM. The proposed method is not only substantial in big data analysis and multivariable problems, but also providing an alternative approach in engineering optimisation.