## 4 Application
### Discussion of the Results  
Figure 6 shows the results from the **robust parameter optimization** for the four concepts (Binding 1a, 1b, 2a, 2b) presented in Figure 5. The quality loss values \(QL_{Fy}\) and \(QL_{Fz}\) represent the concept robustness with respect to the KCs \(F_{y}\) and \(F_{z}\). As already described in Section 4.2, the quality loss value unites the influence of the variance and the mean shift of the respective KC. The multi-objective optimization of the concept Binding 1 with coupled KCs leads to ambiguous results and optimized nominal parameter values that are represented in a Pareto front each for concept 1a and 1b. The inverse relation between \(QL_{Fy}\) and \(QL_{Fz}\) requires the subsequent selection of a suitable trade-off solution with the lowest possible quality loss values. The comparison between Binding 1a and Binding 1b with a reduced number of parameters according to the _Information Axiom_ shows reduced scattering of the KCs and a shift of the Pareto front into an area with lower quality loss values for the simplified concept. This unlocks additional potential. Therefore, the quality loss value for the exemplarily chosen trade-off solutions is reduced from 1470 to 1119 for \(QL_{Fy}\) and from 8043 to 6773 for \(QL_{Fz}\). In a similar way, the robustness of the simplified concept Binding 2b is significantly higher than that of Binding 2a. The comparison of the results of Binding 1 with those of the uncoupled concepts of Binding 2 shows that considering the _Independence Axiom_ results in optimal solutions respectively respective parameter values instead of Pareto fronts with trade-off solutions, see Figure 6. However, a quantitative comparison of the resulting quality loss values between the coupled and uncoupled concepts is not useful for general statements or a proof due to the changed boundary conditions associated with the concept change. Figure 7 shows the initial status for the **tolerance-cost optimization** carried out in addition to the robust parameter optimization discussed above. Considering only the initial tolerance settings from Table A1, the scattering of \(F_{y}\) is significantly lower for the simplified concept alternatives b with fewer parameters contributing to the KC, see Equations (A1), (A3), (A5) and (A7). This effect of the _Information Axiom_ becomes particularly evident in the reduced non-conformance rates \(\hat{z}\) in ppm (parts per million). Figure 6: Parameter design: Optimal results for the four ski binding concepts. This positively affects the subsequent tolerance-cost optimization since the tolerances in the simplified concepts b have to be narrowed to a lesser extent in order to maintain the required quality target. Consequently, the consideration of the _Information Axiom_ in the concept design reduced the optimized total tolerance costs \(C_{\text{sum}}\) from 37.425 (Binding 1a) to 27.008 (Binding 1b) and from 68.135 (Binding 2a) to 48.905 (Binding 2b). This can be explained by the reduced number of components involved resulting in fewer contributors in the determination of the KCs of the concept alternatives b. In tolerance-cost optimization, this means that the tolerances of the individual parameters require fewer limitations in systems with reduced information content, thus leading to lower tolerance costs. Figure 8 shows the optimized tolerance costs for the individual parameters for the four concept alternatives according to Figures A1 and A2. Since a comparison of tolerance costs for individual parameters is not appropriate due to the reallocation that takes place during optimization, the average costs of the parameters are compared. Therefore, the average tolerance cost per parameter for Binding 1 is reduced from 4.165 to 3.865 and for Binding 2 from 5.685 to 5.435. Thus, the application of the _Information Axiom_ also leads to significantly better results in tolerance-cost optimization. However, similar to the robust parameter optimization, a quantitative comparison of the costs between the concepts 1 and 2 is not meaningful.