Taguchi's robust parameter desing calls for simultaneous optimization of the mean and standard deviation responses. The dual response optimization procedures have been adapted to achieve this goal by taking into account both the mean and standard deviation respons functions. The popular formulations of the dual response problem typically impose a restriction on the value of the secondary response (i.e., keeping the standard deviation below a specified value) and optimize the primary response function (i.e., maximize or minimize the mean). Restrictions on the secondary response, however, may rule out better conditions, since an acceptable value of the secondary response is usually unknown. In fact, process conditions that result in a smaller standard deviation are often preferable. A more flexible formulation of the problem can be achieved by considering the secondary response as another primary response. The proposed method will generate more alternative solutions, called Pareto optimal solutions. This gives more flexibility to the decision-maker in exploring alternative solutions. It is also insightful to examine graphically how the controllable variables simultaneously impact the mean and standard deviation. 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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