Robust optimization is a powerful method to find the parameters for a process at which its output is least sensitive to the variation of the input parameters. In this method, measured or estimated noise parameters are used to estimate the scatter of the output. At the optimum design, the variation in noise parameters leads to a minimum scatter of the output. If this minimum scatter of the output does not meet the specified tolerance, then the input noise must be adjusted accordingly. This means for example that materials with a tighter specification must be ordered, which usually incurs additional costs. In this article, an inverse method is presented to tailor the variation of noise parameters based on the allowable tolerance in the output. This method is successfully applied to a non-linear process, lab-type B-pillar part. The results show how to adjust the input noise parameters at a minimum cost to meet the required output tolerance.

A robustness criterion that employs skewness of output is presented for a metamodel-based robust optimization. The propagation of a normally distributed noise variable via nonlinear functions leads to a non-normal output distribution. To consider the non-normality of the output, a skew-normal distribution is used. Mean, standard deviation, and skewness of the output are calculated by applying an analytical approach. To show the applicability of the proposed method, a metal forming process is optimized. The optimization is defined by an objective and a constraint, which are both nonlinear. A Kriging metamodel is used as nonlinear model of that forming process. It is shown that the new robustness criterion is effective at reducing the output variability. Additionally, the results demonstrate that taking into account the skewness of the output helps to satisfy the constraints at the desired level accurately.