Multi-response Robust Parameter Design

Robust parameter design has been widely used in the optimization design of product or process, which effectively improve product quality and obtain great economic benefits. With the differentiation of customer demand for products, multiple quality characteristics often need to be considered in the optimization design of product or process. Therefore, multiple-response optimization design has increasingly shown its important position and role in continuous quality improvement activities. As for multiple-response optimization design, there still exist some problems needed to be resolved. From the current literature, the correlation among quality characteristics is usually ignored by many researchers. As the research going, correlated multi-response optimization design has attracted considerable attentions of many researchers in recent years.In modern manufacturing industry, quality engineers are often required to optimize multiple responses simultaneously. A common approach is to convert multiple responses into a simplified multi-response performance index (MPI) using a technique, such as desirability function, weighted signal-to-noise ratio, grey relational analysis, weighted principal component analysis etc. Then, an optimization method combined with the MPI can be used to find the most desirable parameter setting. However, as the problem grows more complexity, particularly in the situations where the correlation and goal conflict among multiple responses must be considered simultaneously, conventional optimization algorithms can fail to find the global optimum. A new hybrid approach proposed in the paper is to use grey relational analysis in conjunction with principal component analysis (PCA) to obtain the grey relational grade (GRG), and then a process model between the control factor and GRG is performed by BP neural network. Finally, the optimal parameters setting can be found using a hybrid approach combined the global search advantage of genetic algorithm and the local search advantage of pattern search. The paper takes the robust parameter design of correlated multi-response as research subject, and uses construction of the index, process modeling and parameter optimization as research means. The effectiveness of the proposed approach is illustrated by two real industrial examples. The main research conclusions are as follows:(1) The method proposed in the paper has more extensive adaptability, which considers the correlation among multiple responses, the conflict among multiple goals and the robustness of global optimization result simultaneously.(2) Two different approaches combining PCA with GRA are used to deal with two different cases where the number of principal components considered in the PCA-based method is equal to 1 or bigger than 1. Therefore, the problem of robust index for multiple responses is analyzed thoroughly.(3) The paper converts different types of responses into a larger-the-better performance index. The larger the GRG is, the closer multiple quality characteristics approach to ideal performance. Therefore, the proposed method in the paper effectively solves the conflict among multiple responses in the optimization process.(4) During the optimization stage, the proposed hybrid approach combines the global search advantage of GA and the local search advantage of PS, which can effectively improve the ability of global optimization and obtain robust optimal results.