## 4 Discussion  
The proposed DfAM strategy allowed for a significant improvement in dimensional quality, according to the results, was provided in Section 3. The minimum achievable tolerance interval required to fulfil the critical machine performance target was reduced from \(\hat{T}I_{0}~{}=~{}0.555\) mm to \(\hat{T}I_{2}~{}=~{}0.130\) mm. Considering the standard tolerance intervals [43], the application of the proposed DfAM has resulted in a reduction of the achievable tolerance interval from IT14 to IT 11 [43]. Even if the machine performance index is considered instead of the critical one and, consequently, the deviation between the mean value and the target specification is neglected, the achievable tolerance interval is equally reduced from \(\hat{T}I_{0}~{}=~{}0.218\) mm to \(\hat{T}I_{2}~{}=~{}0.093\) mm. Accordingly, considering the \"potential\" performance, the achievable tolerance interval would be reduced from IT12 to IT 10. These results were obtained imposing an objective of 99.73% of the manufactured parts lying within specifications, and a minimum ratio of 1.67 between tolerance interval and results dispersion. Both results demonstrate that the proposed strategy can reduce the average deviation with respect to the target value while simultaneously narrowing down the associated dispersion. The multi-state approach employed for machine performance calculation was key to this achievement since it has allowed to understand and address the relationship between the relative position of part within the tray and the expected quality results. Conversely, although the single-state strategy could be applied without violating repeatability conditions, as it was confirmed by the Barlett's test, the F-test and the test for normality, this approach would lead to a misinterpretation of the causes behind the quality issues. In fact, this interpretation resulted on broader achievable tolerance intervals: \(\hat{T}I_{0}~{}=~{}0.326\) mm from the perspective of machine performance, and \(\hat{T}I_{0}~{}=~{}0.654\) mm from the perspective of the critical machine performance. The observed differences between both strategies are mainly related to the different ways of adjusting the results to the dispersion models. In the proposed cases study, extreme values were not stochastic in a rigorous sense but related to certain locations within the manufacturing tray. Nevertheless, when they were adjusted to a normal distribution under the single-state approach, they contributed to artificially enlarging the dispersion and, consequently, affecting the calculation of the standard deviation, worsening the estimation of the achievable tolerances. Conversely, under the multi-state approach, each location presented a relatively small associated dispersion. The achievable tolerance interval was affected by this dispersion as well as by the difference between extreme states locations (mean values), but the combined effect was still lower than that derived from a single-state perspective. The consequences of the observed differences between both approaches have a relevant influence upon the DfAM strategy. Under the single-state approach, the samples were adjusted to a normal distribution model, with a mean value of 40.164 mm and the standard deviation of 0.0325 mm. Applying a compensation procedure to the design dimension could, in the best situation, center the results around the target (40.000 mm) but this would not have any significant effect upon the dispersion of results. Since a dimensional optimization based on the single-state approach would not affect the sources of variability, the optimized tolerance interval would not be expected to improve the value obtained with the original design and the potential machine performance index (\(\hat{T}I_{0}~{}=~{}0.326\) mm). On the other hand, under the multi-state approach, the position of the part within the tray was identified as a significant source of variability, and the DfAM strategy used this information to individually compensate the design size.