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A Unified Approach for Dual
Response Surface Optimization
L. C. Tang and K. Xu
The optimization of dual response systems in order to achieve better quality has been
an important problem in the robust design of industrial products and processes. In this
chapter, we propose a goal programming approach to optimize a dual response sys-
tem. Theformulationisgeneralenoughtoincludesomeoftheexistingmethodsasspe-
cial cases. For purposes of illustration and comparison, the proposed approach is ap-
plied to two examples. We show that by tuning the weights assigned to the respective
targets for the mean and standard deviation, past results can easily be replicated using
Excel Solver, the use of which further enhances the practical appeal of our formulation.
20.1 INTRODUCTION
1
The dual response surface approach, first considered by Myers and Carter and re-
2
vitalized by Vining and Myers, is important in determining the optimal operating
conditions for an industrial process, so that the target value for the mean of a quality
characteristic is met and its variability is also minimized. Using the approach, some
of the goals of Taguchi’s philosophy can be realized without resorting to combining
information about both mean and variability into a signal-to-noise ratio.
Basically, in the dual response surface approach, two empirical models, one
for the mean and the other for the standard deviation of the response, are first
established, and then the two fitted response surface models are optimized simulta-
neously in a region of interest (x ∈ ). Typical second-order models for the mean and
This chapter is based on the article by L. C. Tang and K. Xu, ‘A unified response for dual response surface
optimization’, Journal of Quality Technology, 34(4), 2002, pp. 437--447, and is reproduced by the permission of
the publisher, the American Society for Quality
Six Sigma: Advanced Tools for Black Belts and Master Black Belts L. C. Tang, T. N. Goh, H. S. Yam and T. Yoap
C 2006 John Wiley & Sons, Ltd
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