# The Relationship between Process Capability and Quality of Measurement System
## 1 Introduction
\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** & & & & & & & & & \\ \hline \(\overline{\pi}\) (mean) & 7.9577 & 7.9593 & 7.9547 & 7.9552 & 7.9571 & 7.9575 & 7.9575 & 7.9579 \\ \hline SD & 0.0062 & 0.0061 & 0.0056 & 0.0065 & 0.0061 & 0.0062 & 0.0095 & 0.0050 \\ \hline Max & 7.9740 & 7.9750 & 7.9713 & 7.9720 & 7.9723 & 7.97267 & 7.9850 & 7.9710 \\ \hline Min & 7.9417 & 7.9473 & 7.9430 & 7.9420 & 7.9450 & 7.9447 & 7.9417 & 7.9477 \\ \hline Distribution & N & N & N & N & N & N & N & \\ \hline \(p\)-value of & & & & & & & & \\ distribution test & 0.5498 & 0.6979 & 0.4096 & 0.6918 & 0.6491 & 0.4269 & 0.4739 & 0.2153 \\ \hline Outliers & & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \multicolumn{8}{c}{Capability Statistics} \\ \hline C\({}_{\rm P}\) & 0.8834 & 0.9855 & 0.8478 & 0.8584 & 0.8136 & 0.9397 & 0.4531 & 1.0519 \\ \hline C\({}_{\rm PL}\) & \(-\)0.0214 & 0.1188 & \(-\)0.2546 & \(-\)0.2156 & \(-\)0.0641 & \(-\)0.0386 & \(-\)0.0204 & \(-\)0.0064 \\ \hline C\({}_{\rm PU}\) & 1.7883 & 1.8522 & 1.9501 & 1.9325 & 1.6914 & 1.9120 & 0.9266 & 2.1102 \\ \hline C\({}_{\rm PK}\) & \(-\)0.0214 & 0.1188 & \(-\)0.2546 & \(-\)0.2156 & \(-\)0.0641 & \(-\)0.0386 & \(-\)0.0204 & \(-\)0.0064 \\ \hline P\({}_{\rm P}\) & 0.5958 & 0.6034 & 0.6550 & 0.5602 & 0.6002 & 0.5949 & 0.3841 & 0.7297 \\ \hline P\({}_{\rm PL}\) & \(-\)0.0144 & 0.0727 & \(-\)0.1967 & \(-\)0.1407 & \(-\)0.0473 & \(-\)0.0244 & \(-\)0.0173 & \(-\)0.0044 \\ \hline P\({}_{\rm PU}\) & 1.2061 & 1.1341 & 1.5067 & 1.2610 & 1.2477 & 1.2142 & 0.7856 & 1.4638 \\ \hline P\({}_{\rm PK}\) & \(-\)0.0144 & 0.0727 & \(-\)0.1967 & \(-\)0.1407 & \(-\)0.0473 & \(-\)0.0244 & \(-\)0.0173 & \(-\)0.0044 \\ \hline \multicolumn{8}{c}{Parts Per Million} \\ \hline ppm \(<\) LSL & 555,556 & 400,000 & 800,000 & 688,889 & 600,000 & 577,778 & 600,000 & 600,000 \\ \hline ppm \(>\) USL & 0 & 0 & 0 & 0 & 0 & 0 & 2222 & 0 \\ \hline ppm Total & 555,556 & 400,000 & 800,000 & 688,889 & 600,000 & 577,778 & 622,222 & 600,000 \\ \hline \multicolumn{8}{c}{Short-Term Defects} \\ \hline ppm \(<\) LSL & 525,614 & 360,784 & 777,517 & 741,134 & 576,252 & 546,094 & 524,450 & 507,630 \\ \hline ppm \(>\) USL & 0.0405 & 0.0138 & 0.0025 & 0.0034 & 0.1946 & 0.0044 & 2719.97 & 0.0001 \\ \hline ppm Total & 525,614 & 360,784 & 777,517 & 741,134 & 576,252 & 546,094 & 527,170 & 507,630 \\ \hline \multicolumn{8}{c}{Overall or Long-Term Defects} \\ \hline ppm \(<\) LSL & 517,282 & 413,638 & 722,458 & 663,525 & 556,407 & 529,220 & 520,732 & 505,293 \\ \hline ppm \(>\) USL & 148.305 & 334.268 & 3.0899 & 77.4525 & 90.8837 & 134.940 & 9220.48 & 5.6315 \\ \hline ppm Total & 517,430 & 413,972 & 72,246 & 663,602 & 556,498 & 529,355 & 529,952 & 505,298 \\ \hline \end{tabular}
\end{table} 
Table 1: Descriptive statistics, capability indices and numbers of noncompliant shafts. To assess the potential capability of a process at a specific point or points in time in order to obtain values within a specification;
2. To predict the future potential of a process in order to create a value within specifications with the use of meaningful metrics;
3. To identify improvement opportunities in the process by reducing or possibly eliminating sources of variability [1]. C\({}_{\rm P}\) and C\({}_{\rm PK}\) are considered short-term potential capability metrics for a process. P\({}_{\rm P}\) is a process index that numerically describes the long-term capability of a process assuming that it was analyzed and stayed in control. It is a simple and straightforward indicator of process performance. It is used when a process is initially starting out [2]. The long-term examination of process capability serves to determine the qualitative capability of the process under real production conditions. It is performed over a longer period (e.g., 20 production days of series production) to take into account all significant effects causing process variability.