# The Relationship between Process Capability and Quality of Measurement System
## 2 Results
### Cohen's Kappa  
To determine the level of agreement, the team used (Cohen's) kappa, which measures the agreement between the evaluations of two metrological appraisers when both are rating the same object. A value of 1 indicates perfect agreement. A value of 0 indicates that agreement is no better than chance. Kappa is only available for tables in which both variables use the same category values and both variables have the same number of categories. Kappa is a measure of interappraiser agreement that tests if the counts in the diagonal cells (the parts that receive the same rating) differ from those expected by chance alone. Kappa is a measure, rather than a test. Kappa takes no account of the size of disagreement between the raters, but only whether they agree or not. When observations are measured on an ordinal categorical scale, a weighted kappa can be used to better measure agreement. Agreement between the two raters is treated as for kappa, but disagreements are measured by the number of categories by which the raters differ [16].  
The measured dimensions of 45 shafts, which were used in the previous section (overall total = 45), were used for testing. The size of each shaft was classified by the metrological appraiser with regard to the required tolerance into one of the three groups, I, II and III, according to the scheme:  
\begin{tabular}{l l} I. & \(\overline{x}<LSL\); \\ II. & \(\overline{x}\in LSL\), \(USL\); \\ III. & \(USL<\overline{x}\). \\ \end{tabular}  
The classification of dimensions for the pair of metrological appraisers A-B, given as an example, is in Table 11. The same procedure was followed for the other pairs of metrological appraisers (a total of 28 combinations of pairs).  
Table 12 shows the agreement/disagreement of metrological appraisers A-B from Table 11. Cell (II-II) contains a number of shaft dimensions that metrological appraisers A and B have equally assigned to group II (e.g., shafts No. 1, 6, 8, \(\ldots\), 43); cell (III-II) contains the number of shafts that metrological appraiser A assigned to group III, but metrological appraiser B to group II (shaft no. 5). Table 12 shows the sum of the shafts by row (row total), column (column total) and the total sum of shafts (overall total = 45). The same procedure was applied to all pairs of metrological appraisers.  
\begin{table}
\begin{tabular}{l l  
The value of [PERSON]'s kappa (\(\kappa\)) for the respective pair of metrological appraisers was calculated using Equation (15).  
\[\kappa=\frac{\sum\ a-\sum\ ef}{overall\ total-\sum\ ef}=\frac{37-22.11}{45-22.11}=0.6 505 \tag{15}\]  
[PERSON]'s kappa values are given in Table 14. If the value of [PERSON]'s kappa (\(\kappa\)) is greater than 0.70, the interappraiser reliability is satisfactory, which means good to excellent agreement.  
According to [PERSON] and [PERSON], the principle states that kappa values less than 0.4 represent poor agreement [26]. This statement is also supported by [16,27].  
Table 14 shows the calculated [PERSON]'s kappa values (\(\kappa\)) for the analyzed pairs of metrological appraisers. A kappa value above 0.7, which indicates good agreement, occurred only for the _EF_ pair (0.73). On the other hand, disagreement was tied to metrological appraisers G and H, with the lowest agreement being between **BG** and **EG**.  
Similar to the individual metrological appraisers, there were large differences between the capability indices C\({}_{\text{P}}\) and P\({}_{\text{P}}\) (Figure 3), and the number of nonconforming products in ppm (Figure 4).