Modeling the uncertainty in response surface methodology through optimization and Monte Carlo simulation: An application in stamping process

Abstract

Among the most frequently used experimental design techniques is the response surface methodology (RSM), which uses an approximation of the real objective function, in the form of an empirical quadratic function. RSM allows the identification of the relations between independent variables (or factors) and a (dependent) response variable. The main contribution of this article is to propose a new procedure that considers the insertion of uncertainties in the coefficients of this empirical function, which is what generally occurs, in practical experimental problems. The new procedure was applied to a real case related to a stamping process in an automotive company, and the results were compared to those obtained by applying classic RSM. The advantages offered by this innovative procedure are presented and discussed, including the statistical validation of the results. The proposed procedure reduces, and sometimes eliminates, the need for additional confirmatory experiments in the laboratory, and allows getting a better adjustment of the factor values and the optimized response variable value compared to the results calculated by classic RSM. It was possible to determine that the proposed procedure outperforms the use of (deterministic) optimization, using the generalized reduced gradient (GRG) algorithm, which is traditionally employed in RSM applications. (C) 2019 Published by Elsevier Ltd.