## 3 Results and Discussion
The plots also exhibit another reference line that shows the overall mean of all measurements. When the reference line is horizontal (parallel to the x-axis), there is no main effect present. The response mean is the same across all factor levels. This particular situation occurs with the factor Step width, which shows that, for the analysis of the variable parallelism, the variation existing in the three levels studied (0.02, 0.22, 0.42) is not significant. On the other hand, when the line is not horizontal, there is a main effect present and the response mean is not the same across all factor levels. In this situation, the steeper the slope of the line, the greater the magnitude of the main effect. In this regard, it is also possible to see from the plot that the three variables have no positive main effects; that is, the plots do not show that by increasing or decreasing a variable's level, the average deviation necessarily increases or decreases all the time. In this regard, the analysis of the Speed factor shows a non-linear behavior. In this case, the highest value of the average is obtained at the level of 2 mm/s. For the remaining levels, the average value drops by around 4 \(\upmu\)m. A similar analysis can be used for the Stylus diameter factor; however, this has an inverse behavior. In this case, the maximum average value is reached during the use of the third factor's level, i.e., Stylus diameter of 8 mm, representing a difference of up to 8 \(\upmu\)m over the average mean value. These results in the plot once more confirm the outcome and conclusions obtained in the ANOVA table where both factors turned out to be significant in the measurement variability of the variable parallelism. On the other hand, Figure 10 shows the interaction between the factors Stylus diameter and Speed on the variable parallelism as an illustrative example. This was selected because it was statistically significant in the 95% confidence interval in the ANOVA table. The significant interaction is indicated by the lack of parallelism of the lines. In general, the behavior of the average varies depending on the interaction of both factors implying that when the measuring Speed is the same, different values will be obtained depending on the Stylus diameter these are measured with. For example, maintaining a constant Speed of 18 mm/s and varying the Stylus diameter from 2 mm to 8 mm yields a measurement value that differs in up to 8 \(\upmu\)m with respect to the initial Stylus diameter level. At the same time, when using the same Stylus diameter, e.g., 2 mm, it is possible to see how changing the Speed of the measurement leads to obtaining three different values that range from 0.2021 mm to 0.2027 mm. As stated in [16], the accuracy indicates the relative closeness of agreement between an experimentally determined value of a quantity and its true value. Standard uncertainties are the difference between the experimentally determined value and truth; thus, as error decreases, accuracy is said to increase. Only in rare instances is the true value of quantity known. Uncertainty (U) estimate, for example, means that the true value of the quantity is expected to be within the \(\pm\)U interval about the experimental value. Figure 9: Main effects plots for parallelism. An analysis of measurement uncertainty that uses components of variance turns out to be an appropriate estimator for the evaluation of Geometrical Product Specifications measurement uncertainty on CMMs. In this regard, Table 5 shows the results of the uncertainty analysis attributed to factors and their interaction. The standard uncertainties of the Stylus diameter, Step width, and Speed variables were determined according to Equations (14)-(16), respectively, while the standard uncertainty of the subsequent interactions was also determined according to Equations (17)-(20), in this particular order.