A Robustness Generalized Distance Function Approach for Multiresponse Robust Optimization

Experimental design with multiple responses has received a great deal of attention from engineers, statisticians and experimenters recently. Generally, robustness and optimization have the same significance in the analysis of a statistical procedure. Compared with much research work on how to simultaneously optimize multiple responses based on certain criteria or objective functions, little research has been done on how robust the optimum solution is. The robustness in this paper refers to low sensitivity of the responses to the fluctuations of the input variables. On the basis of the proposal of a measure of robustness, this paper presents a robustness generalized distance function (RGDF) approach for multiresponse robust optimization, which modifies the generalized distance function (GDF) via a correction matrix. The proposed method takes into consideration of both robustness and optimization. It is illustrated with an example, which shows that the robustness generalized distance function approach gives more robust optimal condition on which multiple responses are simultaneously optimized and insensitive to small changes of input variables.