## 6 Conclusions and Outlook  
The comprehensive comparison of early robust design and robust parameter as well as tolerance-cost optimization with respect to numerous aspects shows that despite the common goal of a robust product design, there are significant differences in wording, starting point, aim and procedure. Despite the awareness of the importance of early robust design, it remains widely unconsidered as the direct effect or advantage for the subsequent robust design steps are often unclear. Thus, the contribution explicitly analyzes the effect of early robust design on robust parameter and tolerance-cost optimization. Since most activities in the robust concept design can be unified under the two axioms of Axiomatic Design, their effect on subsequent optimization is the focus of this article. Together with the findings from the case study, it can be stated that reducing the complexity of a product concept with the help of the _Information Axiom_ has a significant positive effect on the process as well as the results of robust parameter and tolerance-cost optimization. Althoughthe _Independence Axiom_ positively affects the optimization process, the quantitative effect cannot be determined in a generally valid manner, since its implementation is often accompanied by a comprehensive concept change so that comparability is no longer guaranteed. Nevertheless, an uncoupled concept design in the sense of the _Independence Axiom_ with low information content according to the _Information Axiom_ contributes to an overall optimal robust design. In summary, the contribution addresses the specific effect of early robust design on the subsequent steps for the first time, thus bridging the gap between early and late robust design, which strengthens the motivation for an early robustness consideration.  
Further research based on the proposed results could emphasize the significance of the effects. In addition to the pure coupling of functional relations, the effect of contradiction should be analyzed for different cases and optimization problem formulations, especially with regard to the effect on the achieved results. Moreover, further studies with industrial examples would enable a more precise quantification of the effects of the applied axioms and could thus increase the motivation for the practical application of early robust design.  
Conceptualization, S.G., M.R. and B.S.; formal analysis, S.G. and M.R.; funding acquisition, B.S.; investigation, S.G. and M.R.; methodology, S.G., M.R. and B.S.; project administration, B.S.; resources, B.S.; software, M.R.; supervision, B.S.; visualization, S.G. and M.R.; writing--original draft, S.G. and M.R.; writing--review and editing, B.S. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the German Research Foundation (DFG) under the grant number SCHIL 2233/1-3 \"Integrated computer-automated tolerance management in early design stages\".  
Not applicable.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} CAD & Computer-aided design \\ DoE & Design of Experiments \\ KC & Key Characteristic \\ LSL & Lower Specification Limit \\ QL & Quality Loss \\ SNR & Signal-to-Noise Ratio \\ USL & Upper Specification Limit \\ \end{tabular}