Comparison For Experimental Designs And Modeling In Response Surface Methodology

Response surface methodology (RSM) is a collection of modern statistical and mathematical techniques. It is used to investigate the relationship between the response variables and the independent variables. RSM includes response surface design, modeling and optimization. The original response surface model assumes the errors are normally distributed independent random variables with common variance, and the independent variables are measured without errors. However, in reality, the assumptions hold only approximately and it is common to see the independent variable to contain errors or the response data to have outliers. This dissertation mainly studies the robustness of response surface design to the fluctuations of measurement errors and the robustness of response surface model to outliers.This dissertation addresses the basic theories and traditional model estimation methods of response surface methodology, criteria for design comparison, robust estimation and errors-in-variables model, and then it analyses and evaluates the robustness of response surface designs and estimation methods. The detailed research includes the following aspects.Firstly, this study discusses the robustness of the response surface designs to outliers in response data. It includes central composite design involving central composite circumscribed design, central composite face centered design, and Box-Behnken design. On the basis of comparative analysis, the results show outliers in center runs increase the variation in the model residuals and decrease the precision in the prediction of model. For an axial run or corner run outlying, the estimation of quadratic and interation terms are severely influenced, which increase the difficulties of the prediction and optimization of response surface.Secondly, in order to investigate the scaled prediction variances in the errors-in-variables model and compare the performance with those in classic model of response surface designs for three variables, two performance criteria are proposed to evaluate designs with errors in variables. Comparative results have been obtained using simulation studies. For the low level of errors in variables, central composite face-centered design is optimal; otherwise Box-Behnken design has a relatively better performance.Thirdly, the evaluation and comparison of response surface designs using optimality criteria and prediction variance properties are developed for second order designs on spherical regions at the presence of errors in independent variables. In order to have a good visualization of the design robustness to measurement errors, the maximum and minimum scaled prediction variance and fraction of design space plot are proposed and used to compare the designs with or without errors in variables. G-efficiency is calculated for each response surface design. A compromised robust design can be obtained in levels of different factors.Finally, considering the outliers in the response data, this dissertation explores some of the robust methods used for second order response surface model. Various robust fitting methods are studied to examine the impact of the outliers and non-normal distributions on the regression model. A comparative analysis is concluded obtained by applying the regression to simulation and real data.