Effect of Size of the Step in the Response Surface Methodology using Nonlinear Test Functions

The response surface methodology (RSM) is a collection of mathematical and statistical techniques useful in the modeling and analysis of problems in which the dependent variable receives the influence of several independent variables, in order to determine which are the conditions under which should operate these variables to optimize a production process. The RSM estimated a regression model of first order, and sets the search direction using the method of maximum / minimum slope up / down MMS U/D. However, this method selects the step size intuitively, which can affect the efficiency of the RSM. This paper assesses how the step size affects the efficiency of this methodology. The numerical examples are carried out through Monte Carlo experiments, evaluating three response variables: efficiency gain function, the optimum distance and the number of iterations. The results in the simulation experiments showed that in response variables efficiency and gain function at the optimum distance were not affected by the step size, while the number of iterations is found that the efficiency if it is affected by the size of the step and function type of test used.

Authors:

• Jesús Everardo Olguín Tiznado
• Rafael García Martínez
• Claudia Camargo Wilson
• Juan Andrés López Barreras
• Everardo Inzunza González
• Javier Ordorica Villalvazo

Keywords:

• RSM
• dependent variable
• independent variables
• efficiency
• simulation

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