# The Relationship between Process Capability and Quality of Measurement System
## 3 Discussion  
In an organization with higher production and especially with a multi-shift operation, it is usually necessary to employ more metrological appraisers, especially in product inspection. Ideally, there should be no major differences in the quality of their work; thus, they should be mutually replaceable and employable in all positions that require measurement in the organization. The article presents methods commonly used to evaluate the quality of metrological appraisers. [PERSON]'s kappa method, which has a large correlation with the %GRR index (Pearson's coefficient \(\text{r}^{2}=-0.6382\)), as seen in Figure 5, appeared to be the most complex. Figure 6 shows the relationship between the measurement process capability (%GRR) and the proportion of noncompliant shafts (ppm), the proportion of which increased with decreasing measurement capability. Due to the low value of the Pearson coefficient \(\text{r}^{2}=0.3142\), the correlation was moderate, indicating a trend. As the %GGR index increased (and thus the capability of the measurement process decreased), the number of products (shafts and parts) that were discarded as nonconforming increased. However, the measurement was performed on the same products (shafts), so the number of truly non-conforming products was always the same. Incapable, i.e., poor-quality measurement, therefore, led to an overestimation of the number of non-conforming products (shafts), which led to their unnecessary disposal, thereby leading to losses. If a reduction in the %GRR index is achieved by improving the measurement technique, this loss will be reduced. This means that we will not discard shafts that are actually good, but that have been evaluated as nonconforming by poor-quality measurements. Figure 5: Relationship between Cohen’s kappa and %GRR. The results of the analysis of the R&R measurement systems are debatable. The %PV index was not a problem, since, besides the CG pair, the suitability of the used measuring instrument was proven for all other pair combinations. The problem arose when interpreting the %AV and %EV indices, which were components of the %GRR index. As already mentioned, the value of the %AV index increased with increasing disagreement of metrological appraisers. The %EV index depended on the measuring instrument and included two components. The first component was the metrological properties of the instrument (sensitivity, accuracy, precision, uncertainty, systematic bias and stability). These properties were not expected to change during the measurement, i.e., to deteriorate. This component should be handled by a correctly determined calibration interval. The second component was the handling of the measuring instrument, which was related to metrological appraisers. If the instructions for the correct operation of the measuring instrument are not followed, if the metrological appraiser does not have sufficient competence and skill, then the quality of the measuring instrument loses its significance. Since metrological appraisers are living organisms, their measurement results may not be constant. As such they are influenced by physical and mental conditions, not only on their own, but also in a team (a pair of metrological appraisers), and may even be under the influence of drugs or addictive substances [28; 29; 30; 31]. By comparing the results of the individual methods, it can be stated that the best combination was the pair of metrological appraisers E and F (men aged 61 and 32), or pair E and G (male 61 and female 25). In this case, gender and age did not have a statistically significant effect. These three (E, F and G) metrological appraisers were instructed on how to use the micrometer correctly as follows: prior to the measurement, the contact faces must be inspected to exclude the presence of impurities. A ratchet speeder must be used to finalize the tightening, not a thimble sleeve. The same number of \"clicks\" of the ratchet ensures the same pressing force of the jaws between the anvil and spindle faces on the part/shaft.