## 5 Conclusions  
The present work proposes a method for improving the achievable tolerance interval of dimensional features using a multi-state machine performance analysis to feed a design for additive manufacturing strategy. Although the single-state perspective has been commonly used in AM processes, part position within the manufacturing tray is a factor that could significantly affect part quality and this influence should not be neglected. The main conclusions are:  
* Machine performance analysis in AM processes shall be conducted under the multi-state perspective when multiple replicates of a part are going to be manufactured simultaneously in the same tray. This approach is necessary to evaluate if the variability of the deviations of size for a given characteristic is related to the relative position of each replicate within the tray.
* Once the analysis has determined whether the widths and locations of local intrinsic dispersions can be considered homogenous or not, the calculation of the achievable tolerance intervals shall be based on a target value for the performance indexes (\(P_{m}\) and \(P_{mk}\)). The reference value (1.67) shall be used when at least 50 samples are considered, but this value shall be increased for smaller sample sizes.
* Although the optimization of the process is frequently achieved by means of a modification of its configuration, we propose a DfAM compensation procedure that uses the information retrieved from the performance analysis to modify the definition of the design contained in the CAD model. If the measured characteristic shows significant differences regarding the locations of local intrinsic dispersions, this information can be used to particularize the compensation of replicates for the different states (positions) defined. This strategy allows for a reduction of the dispersion of sizes for parts manufactured in the same tray, and for a reduction of the deviation between the mean size of the manufactured characteristic and its target value.
* The application of this methodology to a case study allowed to reduce the achievable tolerance interval from an IT14 to an IT 11 in the case of external cylindrical surfaces with a nominal size of 40 mm and manufactured in a material extrusion machine.  
Results show that the multi-state approach allows for a better understanding of the sources of variation that is crucial to reduce the achievable tolerances. The proposed strategy could help to accelerate industrial adoption of AM processes, especially in those companies with a solid background in precision manufacturing and quality control that incorporate AM machines to enlarge their range of manufacturing capacities. Future research efforts should explore the possible non-linear behavior of the compensation, the extension of the methodology to other AM processes, the possibility of progressive optimization strategies based on the analysis of process capability, and the adaptation of the compensation strategy to geometrical tolerances.  
Conceptualization, N.B.; methodology, N.B. and D.B.; investigation, N.B., B.J.A. and A.N.; writing--original draft preparation, N.B. and D.B.; writing--review and editing, B.J.A. and P.F.; supervision, B.J.A.; project administration, P.F.; funding acquisition, D.B. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Asturian Institute for Economic Development (IDEPA) and ArcelorMittal as part of the RIS3 strategy, grant number SV-PA-15-RS3-4. It has also received funding from the Spanish Ministry of Science, Innovation and Universities (Ministerio de Economia, Industria y Competitividad, Gobierno de Espana--DPI2017-83068-P). The authors wish to thank [PERSON] from Intelmec Ingenieria S.L. for his help.  
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.