Simultaneous optimization of the mean and standard deviation responses is a primary goal of Taguchi's robust parameter design (RPD). The popular formulations of the dual response system (DRS) problem, adapted to achieve this optimization, typically optimize the primary response function, mean, by imposing a restriction (upper limit) on the value of the secondary response, standard deviation. Since an acceptable value for the standard deviation is usually unknown, restriction on the secondary response, however, may rule out better process conditions that result in a smaller standard deviation. The authors propose a more flexible formulation of the problem by considering standard deviation as another primary response, which will generate more alternative solutions called Pareto optimal solutions (POS). Also, examining graphically how the controllable variables simultaneously impact the mean and standard deviation provides a good insight. The procedure is illustrated with three examples, using both the NIMBUS software for nonlinear multiobjective programming and the solver in the Excel spreadsheet.
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