## 3 Results
### Calculation of \(\hat{T}I_{0}\) under the Single-State Perspective  
An alternative calculation of \(\hat{T}I_{0}\) was performed considering the single-state hypothesis. This approach would require the parts to be manufactured in an uninterrupted run under normal operating conditions and repeatability conditions [34]. The usual recommendation is that the study should be conducted with no less than 30 specimens, maintaining constant all factors others than the machine, like the operator or the batch of material, while avoiding intermediate operations like warm-up times. These conditions are specially challenging in MEX processes for several reasons: first, these processes have usually a very slow cycle time; second, raw material is provided in small-volume coils (typically ranging from 0.5 kg to 3 kg), which makes it difficult to manufacture series of big parts from the same coil; third, the manufacturing tray is often extracted from the machine to remove the parts, and this could lead to carry out operations (warm-up, tray levelling) that could cause a disturbance on repeatability conditions. To deal with this difficulty, results from different trays were analysed to evaluate if parts could be treated as if they were a sample of a single population. Consequently, the hypothesis of homogeneity of the variances and the means were sequentially verified. The hypothesis of homogeneity of variances was tested in first place using the Bartlett's test. The calculated \(p\)-value was 0.983, much greater than the significance value of 0.05, which indicates that the variances can be considered equal (Figure 7a). Then, the [PERSON]'s method was applied to evaluate whether pairs of means were different between consecutive trays (Figure 7b). The calculated \(p\)-values were found to be higher than the 0.05 level of significance for each pair of trays within the comparison [Table 4]. Figure 7b shows that the calculated intervals overlapped, containing the zero, which indicates that there is no statistical evidence for the means to be significantly different. It was concluded that the trays have no statistically significant effect upon the means of the measured sizes. The combination of this result with the equality of variances allows for the conclusion that the different trays can be considered as part of a single population and, consequently, the application of the ISO 22514-3 [34] did not violate the repeatability hypothesis. Figure 6: Representation of \(\hat{T}I_{0}\) and the individual distributions per state calculated under the multi-state perspective: upon the original design: (**a**) Calculated to assess the target performance index; (**b**) Calculated to assess the target critical performance index. Given this result, the production was onwards assumed to come from a single batch, and the machine performance analysis continued with the identification of the actual distribution. An Anderson-Darling normality test was used to determine if the distribution of values was normal or not. This test compares the empirical cumulative distribution function of the measured data with the expected results of a normal distributed data. The \(p\)-value was 0.271, higher than the \(\alpha\)-level (0.1), which indicates that the hypothesis of the data following a normal distribution cannot be rejected (Figure 8). The mean value was \(\overline{x}~{}=~{}40.164\) mm and the standard deviation was \(s~{}=~{}0.0325\) mm. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Difference** & **Difference** & **SE of** & **95\% CI** & **T-Value** & **Adjusted** \(p\)-Value** \\ \hline T2—T1 & \(-\)0.0086 & 0.0127 & (\(-\)0.0342; 0.0170) & \(-\)0.68 & 0.501 \\ T3—T1 & 0.0032 & 0.0127 & (\(-\)0.0224; 0.00287) & 0.25 & 0.805 \\ T4—T1 & 0.041 & 0.0127 & (\(-\)0.0115; 0.0396) & 1.11 & 0.272 \\ T3—T2 & 0.0118 & 0.0127 & (\(-\)0.0138; 0.0373) & 0.93 & 0.359 \\ T4—T2 & 0.0227 & 0.0127 & (\(-\)0.0029; 0.0483) & 1.78 & 0.081 \\ T4—T3 & 0.0109 & 0.0127 & (\(-\)0.0146; 0.0365) & 0.86 & 0.395 \\ \hline \end{tabular}
\end{table}