## 5 Results
### Analysis of Rope in the Third Quality Class  
Table 3 shows that the maximum tensile strength values of all three tested wires exceed the upper specific limit (USL = 1695.6 MPa). The defined nominal accuracy for ropes in the third quality group is set within the interval \(\langle 1570;\ 1695.6\rangle\) MPa. The target value of nominal accuracy for the third quality class is 1632.8 MPa. Wire No. 1 exhibits the highest variation range (V\({}_{\rm x}\) = 170.06 MPa) and also the highest standard deviation (s = 38.95 MPa), indicating considerable variability in wire strength. The corresponding dispersion value (s\({}^{2}\) = 1516.77) confirms significant fluctuations in the measured tensile strength values. The average strength value for wire No. 1 is 1714.38 MPa; it can be stated that it significantly exceeds the target value of nominal accuracy. Similarly, Wire No. 3 also shows elevated variability, with a variation range of V\({}_{\rm x}\) = 159.24 MPa and a standard deviation of s = 32.75 MPa. From the perspective of tensile strength performance, the measured values reflect the characteristic strength associated with steel ropes of the third quality class, specifically type 42.5 6x39 NFC 1570 B zZ. To assess the statistical validity of the control charts and capability indices, the Anderson-Darling test for normality was applied to all rope samples, following the procedure described in Section 4.1.1. Figure 7 shows the strength distribution of wires from a Class III rope (42.5 6x39 NFC 1570 B zZ). A considerable portion of values exceed the upper specification limit (1695.6 MPa), indicating poor centering and high variability. The shape of the histogram clearly rejects the hypothesis of a normal distribution, and this is further supported by the \(p\)-value < 0.005 reported in Figure 8, which confirms a statistically significant deviation from normality. Figure 7 illustrates that the majority of values are concentrated within the interval \(\langle 1675;\ 1685\rangle\) MPa. Although the measured wire strength values fall within the specified specific limits \(\langle 1570;\ 1695.6\rangle\) MPa, the nominal accuracy interval is not entirely satisfied, as only 126 values lie within this range. The target value of 1632.8 MPa, which falls within the \(\pm 4\%\) tolerance band, highlights a centering issue in the data. In total, 46.15% of the measured values (108 values) lie outside the specified limits, suggesting a significant misalignment of the process center and potential quality nonconformities in the rope's performance. Figure 8 clearly indicates that the measured wire strength values fall outside the nominal accuracy interval of \(\langle 1570;\ 1695.6\rangle\) MPa. Given that the assumption of normal distribution is not fulfilled, the calculation of capability indices (C\({}_{\rm p}\), C\({}_{\rm pk}\)) is not recommended, as it would yield misleading or invalid results. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Wire 1** & **Wire 2** & **Wire 3** \\ \hline Arithmetic mean [MPa] & 1714.38 & 1686.46 & 1674.37 \\ Maximum value [MPa] & 1802.67 & 1751.65 & 1751.59 \\ Minimum value [MPa] & 1632.60 & 1632.60 & 1592.36 \\ Variation range (V\({}_{\rm x}\)) [MPa] & 170.06 & 119.04 & 159.24 \\ Standard deviation (s) [MPa] & 38.95 & 29.98 & 32.75 \\ Variance (s\({}^{2}\)) [MPa] & 1516.77 & 898.87 & 1072.45 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical analysis of the strength of three wires from third-quality-class rope. Based on the data presented in Figures 7 and 8, it can be concluded that the measured strength values for wires No. 1 and No. 3 exceed the upper specific limit (USL = 1695.6 MPa). This further confirms the misalignment and inconsistency in the strength distribution of the assessed wires. Figure 8: Control chart showing process stability for a third-quality-class rope (3 wires). Figure 7: Histogram and capability analysis of wire strength in a third-quality-class rope (3 wires).