## 4 Conclusions  
The present paper addressed the important topic of uncertainty analysis in the case of CMM. The main goal aimed at analyzing and quantifying the influence of key factors and their interactions on the measurements' uncertainty of defined variables. The paper started with an analysis of related literature and subsequently proceeded to the design and implementation of a Random Factorial Design of Experiments that took into consideration factors like the Stylus diameter, Step width, and Speed, using three levels each.  
The investigation allowed estimating the uncertainty of the CMM measurement using statistical methods such as the DOE with random factors and the ANOVA. The application made in the measurement of five variables (parallelism, angularity, roundness, diameter, and distance) offered relevant information on the performance of the CMM and its accuracy based on the variation of the studied factors through their random levels. The ANOVA results showed a strong interaction among the factor Stylus diameter, Step width, and Speed, meaning that a noticeable variation in the mean measurement error was generated when changing the levels of these factors simultaneously.  
The highest value of standard uncertainty was associated with the Stylus diameter of 8 mm in the evaluation of the variable's angularity and diameter. In this case, it meant that any change related to its levels would influence the uncertainty in a value that could reach up to 8.73 \(\upmu\)m and 6.63 \(\upmu\)m, respectively. In the case of the Speed factor, it has the biggest influence on the measurement and evaluation of a form parameter (roundness) reaching up to 4.66 \(\upmu\)m.  
The findings and results obtained by the experimental investigation can be taken as a reference for more optimized use of the factor and their levels in the measurement of the Geometrical Products Specifications under question, and this in order to face lesser values of the uncertainty. In practical terms, these results can be used, for example, to reduce the time spent in the measurements that leads to increased productivity in the measuring of Geometrical Products Specifications, e.g., by using higher speeds in the scanning of the measured part.  
In the end, besides all previous elements, the authors believe this paper contributes to a better and more flexible use and comprehension of the factors, their interactions, and the variables analyzed, all this in the context of the ZEISS CenterMax CMM.  
Conceptualization, M.K., D.R.D.S., and L.C.M.; methodology, M.K. and D.R.D.S.; validation, M.K., D.R.D.S., and L.C.M.; formal analysis, L.C.M. and D.R.D.S.; investigation, M.K., L.C.M., A.A.L.C., and R.H.; resources, M.K.; writing--original draft preparation, D.R.D.S. and L.C.M.; writing--review and editing, D.R.D.S.; visualization, D.R.D.S. and M.K.; project administration, D.R.D.S. and M.K.; funding acquisition, D.R.D.S. and M.K. All authors have read and agreed to the published version of the manuscript.  
This work was funded by the Slovak Research and Development Agency under the Contract no. APVV-18-0418.  
This work was supported by the Slovak Research and Development Agency under the Contract no. APVV-18-0418: \"Research on causes of geometrical deviations in the production of seamless tubes and their technological inheritance with emphasis on the shape stability of precision cold drawn tubes using metrological systems\". This support is gratefully acknowledged.  
The authors declare no conflicts of interest.