A Fuzzy Programming for Optimizing Multi Response Surface in Robust Designs

Optimization of multi response surface (MRS) in robust designs is applied to determine optimum characteristics of a process in a satisfactory region and reduce variation of responses. In this paper, a methodology is proposed for optimizing multi response surface in robust designs, which optimizes mean and variance simultaneously by applying fuzzy set theory. At first, a method is proposed to constitute a regression model based on replicates of a response and aggregate regression models so that a fuzzy regression model expresses each response. The obtained regression model includes fuzzy coefficients which consider uncertainty in the collected data. Then a multi objective decision making (MODM) problem is used. After introducing deviation function based on robustness concept and using desirability function, a two objective problem is constituted. At last, a fuzzy programming method is expressed to solve the problem by applying degree of satisfaction from each objective. Then the problem is converted to a single objective model with the goals of increasing desirability and robustness simultaneously. The obtained model has the capability of assigning importance weight for each goal based on decision making preferences. Solving the model, the obtained optimum factor levels are fuzzy numbers so that a bigger satisfactory region could be provided. Finally, a numerical example is expressed to illustrate the proposed methodology. © 2009 World Academic Press, UK. All rights reserved.