Response surface modeling and optimization in multiresponse experiments using seemingly unrelated regressions

Response surface methodology (RSM) is widely used for optimizing manufacturing processes and product designs. Most applications of RSM involve several response variables. In a typical RSM study, the experimenter will build an empirical model such as the second-order model to each response and use these models to determine settings on the design variables that produce optimal or at least acceptable values for the responses. In most multiple-response RSM problems, the experimenter fits a model to each response using ordinary least squares (OLS). This article illustrates another estimation technique useful in multiple-response RSM problems, seemingly unrelated regressions (SUR). This technique can be very useful when response variables in a multiple-response RSM problem are correlated. Essentially, SUR produces more precise estimates of the model parameters than OLS when responses are correlated. This improved precision of estimation can lead to a more precise estimate of the optimum operating conditions on the process.