Optimization For Multiple Responses Based On Goodness Of Fit For Response Surface Model

RSM(Response Surface Methodology) is an effective design of experiment method to improve products’quality. For multiple-response optimization problem, the reliability of optimization result can be impacted by different goodness of fit of the repsonse surface models. Therefore, this thesis does the research on optimization method for multiple responses based on goodness of fit for response surface.The thesis first introduces some basic theories and application methodologies of response surface method. Then some multiple response surface optimization methods are described, including Mahalanobis distance method, quality loss functin method, traditional desirability function method, etc. Assessments are made on these common methods as well.For the common multi-response surface optimization methods above don’t consider goodness of fit of the regression models, or multi-repsonse surface optimization problem cann’t be well solved in these methods, the thesis does researh on this aspect. Reliable statistic index to measure the goodness of fit for repsonse surface model should be discussed as a premise. Neither of R2 or R2adj can well measure the regression degree of models. Another rational statistic, Rnl can be used to measure the goodness of fit of a regression model.After that, the thesis uses the traditional desirability function and the exponetial desirability function defined by Kim and Lin for reference, and proposes a modified desirability funtion method. Finally, two cases are solved by the new desirability function method, considering goodness of fit of response surface models. The new method can be applied in multiple response problems.