# Management System According to ISO/IEC 17025: Method Validation
## 3 Results  
The results of applying the anchor test in mine A, with 3 operators and 20 tests each, are presented in Table 3.  
According to the Anova method used to conduct repeatability and reproducibility studies to assess measurement system quality control, if the % r&R is less than 10%, the measurement system is deemed acceptable for mine A. Additionally, this considers an uncertainty of \(\pm\)2.2 tons and a coverage factor (k) of 2 for a confidence interval of 95.45% [13]. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Variation** & **Sum of Squares** & \
\begin{tabular}{l} **Degrees of** \\ **Freedom** \\ \end{tabular} &
\begin{tabular}{l} **Mean** \\ **Squares** \\ \end{tabular} \\ \hline Operator (o) & SSo & \(\mathrm{o}-1\) & \(\mathit{MSo}=\frac{SSo}{(o-1)}\) \\ Item (i) & SSi & \(\mathrm{i}-1\) & \(\mathit{MSi}=\frac{SSi}{(i-1)}\) \\ Operator \(\times\) item (oi) & SSoi & \(\mathrm{(o}-1)\mathrm{(i}-1)\) & \(\mathit{MSoi}=\frac{-SSoi}{(o-1)(i-1)}\) \\ Error & SSe & \(\mathrm{oi}\mathrm{(t-1)}\) & \(\mathit{SMo}=\frac{SSo}{\mathrm{oi}(t-1)}\) \\ Total & SSt & \(\mathrm{oit}-1\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Standard ANOVA. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variation Source** & **Sum of Squares** & \
\begin{tabular}{l} **Degrees of** \\ **Freedom** \\ \end{tabular} &
\begin{tabular}{l} **Mean** \\ **Squares** \\ \end{tabular} & **F-Reason** & \(\boldsymbol{p}\)**-Value** \\ \hline Operator & 0.016 & 2 & 0.0080 & 18.42 & 0.00002 \\ Items & 0.610 & 9 & 0.0701 & & \\ Interaction & 0.960 & 18 & 0.0540 & & \\ Error & 1.400 & 30 & 0.0470 & & \\ Total & 2.991 & 59 & - & & \\ \hline Repeatability & 1.11 & & \% Rep. & 9.2 & \\ Reproducibility & 0.25 & & \% Play\_ & 2.0 & \\ Interaction & 0.30 & & \%Interaction & 2.5 & \\ r\&R & 1.18 & \%r\&R & 9.52 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: ANOVA table and r&R results for mine A. The results of the anchor test conducted in mine B, involving 3 operators and 20 tests each, are presented in Table 4.  
Additionally, the Shapiro-Wilk normality test indicated a normal distribution for both mine A (with a value of 0.822) and mine B (with a value of 0.866). The results of the Kolmogorov-Smirnov test were not considered due to the small sample size (n < 50). It is worth noting that the Shapiro-Wilk test is generally more sensitive for detecting deviations from normality in small samples, while the Kolmogorov-Smirnov test is more suitable for larger samples. According to the Anova method employed for conducting repeatability and reproducibility studies to assess measurement system quality control, if the % r&R is less than 10%, the measurement system is considered acceptable for mine B. This assessment is made considering an uncertainty of \(\pm\)2.3 tons and a coverage factor (k) of 2 for a confidence interval of 95.45% (measured according to the guidance of the expression of uncertainty in measurement, ISO 1993) (refer to Figure 5). The results for the inter-laboratory experimental design comparison, developed in mine A with employees from 'Mining Industry X' who agreed to participate, are presented. The test involved the use of anchors of 5/8 with three operators, utilizing the same measuring instrument previously calibrated and used in mine A. These results are detailed in Table 5 and Figure 6. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variation Source** & **Sum of Squares** &
\begin{tabular}{c} **Degrees of** \\ **Freedom** \\ \end{tabular} & **Mean Squares** & **F-Reason** & **\(p\)-Value** \\ \hline Operator & 0.076 & 2 & 0.0381 & 12.72 & 0.00001 \\ Items & 0.730 & 9 & 0.0801 & & \\ Interaction & 0.870 & 18 & 0.0480 & & \\ Error & 1.490 & 30 & 0.0500 & & \\ Total & 3.171 & 59 & - & & \\ \hline Repeatability & 1.15 & & \% Rep. & 9.4 & \\ Reproducibility & 0.12 & & \% Play\_ & 1.0 & \\ Interaction & 0.13 & & \%Interaction & 1.1 & \\ r\&R & 1.16 & & \%r\&R & 9.52 \\ \hline \hline \end{tabular}
\end{table}