Robust parameter design based on Kullback-Leibler divergence

Robust parameter design (RPD) is an effective approach used to improve the quality of products and processes. Traditional RPD assumes that the distribution of the uncontrollable factors (noise variables) is known, and then selects the levels of the controllable variables that minimize the variation imposed on the process through the noise variables while optimizing a defined quality characteristic. However, the distribution of the noise variables is often unknown in practice, using improper distribution assumptions may lead to biased optimization results with poor performance. In this paper, a novel methodology is proposed from the perspective of robust optimization, regarding the distribution of the noise factor as an uncertainty variable. Based upon the data, a family of noise distributions can be established via KL divergence, and then a KL-based robust parameter design (KL-RPD) approach is developed. It is shown that the proposed methodology outperforms the existing methods. Our methodology can be applied to any kinds of metamodel, to problems with any high-dimensional noise factors, and has more accurate results than the other approaches. Two examples are utilized to illustrate these advantages.