## 4 Discussion
This strategy reduced the inter-location variability (Figure 12), resulting on an improvement of the achievable tolerance intervals. The question of part location is not frequent in studies employing benchmarking artifacts [10; 12; 51] because their objectives have more to do with comparison between different processes or machines or with the analysis of the influence of process parameters than with a general assessment of their capabilities. The use of the term \"capability\" in some works [10] could lead to misunderstandings if the results obtained with a benchmark artifact are erroneously considered as a reference for the expected quality of a new production. In fact, the ISO 22514-1 [26] establishes that capability or performance analysis should be conducted for each characteristic individually, as the non-fulfilment of a single specification could make the whole part to be rejected. Quality prediction would require of complex modelling because AM is subjected to multiple sources of variability. Conversely, running a performance or capability study is an adequate strategy to analyze and fix quality issues for medium-to-large production batches. The rejection of S12 in the optimized trays was determined after checking its behavior as an outlier. The reasons for this anomalous behavior were found in the values of trays 5 and 6 that were used to calculate C\({}_{j}\). Regarding S12, the difference between results in tray 5 and tray 6 (Table 5) were the highest among all measured values (0.026 mm). This was also the case of the differences observed for S12 within the four original trays (Table 2), which indicates that this specific location (0; \(-\)67.5) was subjected to a higher variability. Even when the [PERSON]'s test did not consider this variability to be significantly different than the rest, this result could indicate that the compensation for S12 would require of more replicates to improve its accuracy. In any case, the multi-state approach allowed for the identification of such abnormal behavior and the adoption of further decisions on production arrangement. The use of a sensibility coefficient C was necessary to properly compensate the observed deviations. The first set of compensated trays (Table 4) showed a significant reduction in the deviation between the absolute mean value of the manufactured set and the target one (from 0.164 mm to 0.040 mm), but this value was improved after the calculation of the C\({}_{j}\) and the manufacturing of the optimized trays (0.019 mm). It was observed that the relationship between the variation applied to the design diameter (input) and the measured variation of the manufactured diameters (output) was neither directly proportional nor independent from the state (location) of the part. This conclusion is also relevant for future works, since those DfAM strategies, based on modelling size deviations and applying a compensation to the CAD file, should also consider the possibility of the response being position-dependent. Moreover, although the result was very close to the target value, there was still room for further improvement. Even after recalculating the sensitivity coefficients, results obtained from optimization did not exactly match the target values. This fact points out that the calculation of those coefficients could be even more complex than expected. Considering the results, the obtained values pointed towards a non-linear behavior, which is also a question of interest for further research. Figure 12: Results of the multi-state DfAM strategy: (a) Original design; (b) Optimized designs. As it was discussed before, capability analyses are hardly comparable between different geometries, processes, or configurations [35; 38; 39]. Nevertheless, once the production parameters have been set, attention should be drawn to those factors related to production decisions, with a special focus on the arrangement of parts within the manufacturing tray.