From specified product tolerance to acceptable material and process scatter: an inverse robust optimization approach

Abstract Production efficiency in metal forming processes can be improved by implementing robust optimization. In a robust optimization method, the material and process scatter are taken into account to predict and to minimize the product variability around the target mean. For this purpose, the scatter of input parameters are propagated to predict the product variability. Consequently, a design setting is selected at which product variation due to input scatter is minimized. If the minimum product variation is still higher than the specific tolerance, then the input noise must be adjusted accordingly. For example this means that materials with a tighter specification must be ordered, which often results in additional costs. In this article, an inverse robust optimization approach is presented to tailor the variation of material and process noise parameters based on the specified product tolerance. Both robust optimization and tailoring of material and process scatter are performed on the metamodel of an automotive part. Although the robust optimization method facilitates finding a design setting at which the product to product variation is minimized, the tighter product tolerance is only achievable by requiring less scatter of noise parameters. It is shown that the presented inverse approach is able to predict the required adjustment for each noise parameter to obtain the specified product tolerance. Additionally, the developed method can equally be used to relax material specifications and thus obtain the same product tolerance, ultimately resulting in a cheaper process. A strategy for updating the metamodel on a wider (noise) base is presented and implemented to obtain a larger noise scatter while maintaining the same product tolerance.