# The Relationship between Process Capability and Quality of Measurement System
## 2 Results
### Measurement System Analysis  
The R&R (repeatability and reproducibility) method was used again to calculate the capability of the measurement system, comprising 8 metrological appraisers and 45 shafts. Dimension d\({}_{2}\) was measured. The measurement was repeated three times in random order of the metrological appraisers and shafts. Capability was calculated for pairs of metrological appraisers by Quantum XL software according to the procedure described in more detail in [16]. The data sets of all metrological appraisers showed a normal distribution, with no outliers. The control charts showed that the processes were not in a statistically controlled state. This could, to some extent, affect the reliability of the shaft production process indices of C\({}_{\text{P}}\) and P\({}_{\text{P}}\), which are given in Table 1. A process that is not under statistical control may, to some extent, also affect the values of the measurement system (and process) capability indices--the values are given in Tables 7-10. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Metrological** & **A** & **B** & **C** & **D** & **E** & **F** & **G** & **H** \\
**Appraiser** & **A** & **B** & **C** & **D** & **E** & **F** & **G** & **H** \\ \hline \(\overline{x}\) & 31; 42 & 31 & 31; 42 & 31; 42 & 31 & 26; 31 & 4 & 33 \\ \hline MR & - & - & - & - & - & - & - & 4 & 5; 33 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Shafts out of control limits indicated by \(\overline{x}\) and MR control charts (the shaft No. ). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**B** & **C** & **D** & **E** & **F** & **G** & **H** & \\ \hline
22.76 & **35.01** & 19.31 & 24.59 & 21.16 & **52.93** & **34.30** & A \\ \hline  & 27.21 & _10.62_ & _16.21_ & _12.62_ & **49.11** & 25.83 & B \\ \cline{2-7}  & & 27.32 & **31.15** & 27.35 & **57.21** & **39.33** & C \\ \cline{2-7}  & & & _13.11_ & _9.34_ & **45.90** & 19.65 & D \\ \cline{2-7}  & & & & _14.59_ & **51.06** & 28.21 & E \\ \cline{2-7}  & & & & & **48.32** & 23.75 & F \\ \cline{2-7}  & & & & & & **57.19** & G \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Values of %EV (%). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**B** & **C** & **D** & **E** & **F** & **G** & **H** & \\ \hline
**0.0047** & **0.0** & **0.0** & 0.2950 & _0.7666_ & _0.8593_ & _0.7830_ & A \\ \hline  & **0.0** & **0.0** & **0.0** & **0.0** & 0.1848 & 0.1054 & B \\ \cline{2-7}  & & **0.2049** & **0.0** & **0.0** & **0.0215** & **0.0001** & C \\ \cline{2-7}  & & & **0.0003** & **0.0** & 0.1057 & **0.0020** & D \\ \cline{2-7}  & & & & 0.3206 & _0.7939_ & 0.4044 & E \\ \cline{2-7}  & & & & _0.9744_ & _0.6811_ & F \\ \cline{2-7}  & & & & & _0.7418_ & G \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Paired \(t\)-test, \(p\)-values and gross/red numbers showing a statistically significant difference. The %EV index quantifies the effect of the measuring instrument. Although the same measuring instrument was used for all measurements, its effect was not constant, as shown in Table 7. Metrological appraisers **G** and **C** showed a high degree of remoteness. The pairs of metrological appraisers _DF_, _BD_, _BF_, _DE_, _EF_ and _BE_ showed a high degree of agreement. The _DF_ pair showed the smallest difference. Metrological appraiser F was the most appropriate for this analysis. The %AV index quantified the impact of the difference between metrological appraisers. A higher value indicated higher \"disharmony\" between the appraisers in the group. The index values are provided in Table 8. A high degree of remoteness was found in appraiser **C**. Complete agreement was found for the metrological appraisers _AG_, _AH_, _EG_, _FG_ and _GH_. A negligible difference was found for the pairs _AF_, _EF_, _FH_, _CD_, _AE_, _EH_, _AB_ and _BH_. Metrological appraisers A, G and E appeared to be the most appropriate for this analysis.