Robust Optimization in Quality Engineering

Abstract

Quality engineers often face the job of identifying process or product design parameters that optimize performance response. The first step is to construct a model, using historical or experimental data, that relates the design parameters to the response measures. The next step is to identify the best design parameters based on the model. Clearly, the model itself is only an approximation of the true relationship between the design parameters and the responses. The advances in optimization theory and computer technology have enabled quality engineers to obtain a good solution more efficiently by taking into account the inherent uncertainty in these empirically based models.

Two widely used techniques for parameter optimization, described with examples in this chapter, are the response surface methodology (RSM) and Taguchi loss function. In both methods, the response model is assumed to be fully correct at each step. In this chapter we show how to enhance both methods by using robust optimization tools that acknowledge the uncertainty in the models to find even better solutions. We develop a family of models from the confidence region of the model parameters and show how to use sophistical optimization techniques to find better design parameters over the entire family of approximate models.

Section 12.1 of the chapter gives an introduction to the design parameter selection problem and motivates the need for robust optimization. Section 12.2 presents the robust optimization approach to address the problem of optimizing empirically based response functions by developing a family of models from the confidence region of the model parameters. In Sect. 12.2 robust optimization is compared to traditional optimization approaches where the empirical model is assumed to be true and the optimization is conducted without considering the uncertainty in the parameter estimates. Simulation is used to make the comparison in the context of response surface methodology, a widely used method to optimize products and processes that is briefly described in the section. Section 12.3 introduces a refined technique, called weighted robust optimization, where more-likely points in the confidence region of the empirically determined parameters are given heavier weight than less-likely points. We show that this method provides even more effective solutions compared to robust optimization without weights. Section 12.4 discusses Taguchiʼs loss function and how to leverage robust optimization methods to obtain better solutions when the loss function is estimated from empirical experimental data.