Integrated Robust Design Using Response Surface Methodology and Constrained Optimization
Chen, Lijun Jay
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System design, parameter design, and tolerance design are the three stages of product or process development advocated by Genichi Taguchi. Parameter design, or robust parameter design (RPD), is the method to determine nominal parameter values of controllable variables such that the quality characteristics can meet the specifications and the variability transmitted from uncontrollable or noise variables is minimized for the process or product. Tolerance design is used to determine the best limits for the parameters to meet the variation and economical requirements of the design. In this thesis, response surface methodology (RSM) and nonlinear programming methods are adopted to integrate the parameter and tolerance design. The joint optimization method that conducts parameter design and tolerance design simultaneously is more effective than the traditional sequential process. While Taguchi proposed the crossed array design, the combined array design approach is more flexible and efficient since it combines controllable factors, internal noise factors, and external noise factors in a single array design. A combined array design and the dual response surface method can provide detailed information of the process through process mean and process variance obtained from the response model. Among a variety of cuboidal designs and spherical designs, standard or modified central composite designs (CCD) or face-centered cube (FCC) designs are ideal for fitting second-order response surface models, which are widely applied in manufacturing processes. Box-Behnken design (BBD), mixed resolution design (MRD), and small composite design (SCD) are also discussed as alternatives. After modeling the system, nonlinear programming can be used to solve the constrained optimization problem. Dual RSM, mean square error (MSE) loss criterion, generalized linear model, and desirability function approach can be selected to work with quality loss function and production cost function to formulate the object function for optimization. This research also extends robust design and RSM from single response to the study of multiple responses. It was shown that the RSM is superior to Taguchi approach and is a natural fit for robust design problems. Based on our study, we can conclude that dual RSM can work very well with ordinary least squares method or generalized linear model (GLM) to solve robust parameter design problems. In addition, desirability function approach is a good selection for multiple-response parameter design problems. It was confirmed that considering the internal noise factors (standard deviations of the control factors) will improve the regression model and have a more appropriate optimal solution. In addition, simulating the internal noise factors as control variables in the combined array design is an attractive alternative to the traditional method that models the internal noise factors as part of the noise variables. The purpose of this research is to develop the framework for robust design and the strategies for RSM. The practical objective is to obtain the optimal parameters and tolerances of the design variables in a system with single or multiple quality characteristics, and thereby achieve the goal of improving the quality of products and processes in a cost effective manner. It was demonstrated that the proposed methodology is appropriate for solving complex design problems in industry applications.