## 3 Problem Formulation
To evaluate wire quality, we established a classification criterion centered on strength class dispersion. Specifically, we adopted a tolerance of \(\pm 4\%\) from the mean strength value as the benchmark for high-quality wire consistency within a rope structure. This threshold was derived from long-term empirical observations of ropes demonstrating superior performance and minimal wire strength dispersion. Although not defined in current standards, this reflects the best practices observed in high-grade industrial applications. For the purpose of this analysis, steel ropes from actual industrial applications were selected, all operating under comparable conditions during the period from 2000 to 2025. This extended time frame was chosen to assess the practical impact of the implementation of the EN 12385 standard, introduced in 2008. A total of 112 steel wire ropes were evaluated. Tensile strength tests were conducted on 100% of the wires from each rope. Based on the results, the ropes were classified into four quality classes. For classification purposes, a rope was permitted to have a maximum of three wires outside the specified tolerance interval without disqualifying it from a given class. The classification of rope classes is as follows [16]:  
* Class I included ropes that met the highest quality standard, with wire strength class dispersion within \(\pm 4\%\) of the mean--representing optimal selection of input material;
* Class II comprised ropes that conformed to the criteria set by the now obsolete DIN 21254 or STN 02 4301 standards, with a strength class dispersion tolerance of \(\pm 10\%\);
* Class III included ropes meeting the current EN 12385-1 requirements, which allow for a dispersion range of \(-50\) MPa to +15%;
* Class IV consisted of ropes that failed to meet the minimum requirements defined by EN 12385-1. Figure 1 illustrates the distribution of ropes into quality class. Nearly 44% were categorized into Class I, while around 24% fell into the lowest quality categories (Class III and IV), reflecting broader dispersion in wire strength. This chart illustrates the distribution of steel rope quality classes by year of production (Figure 2). It highlights a significant increase in lower-quality ropes (Classes III and IV) after the adoption of the EN 12385-1 standard in 2008, suggesting an impact of broader tolerance thresholds on manufacturing quality. Notably, 27 ropes (24.1%) exhibited strength class dispersion wider than the limits prescribed by the now obsolete standards (DIN 21254 and STN 02 4301), and were thus considered to be of lower quality. A key finding from the analysis is the significant increase in the number of ropes falling into Classes III and IV following the implementation of EN 12385-1 in 2008, which introduced a broader tolerance for wire strength class dispersion. Of the 27 ropes classified in Classes III and IV, 22 were manufactured after 2008, and only 5 were produced before that year. Specifically, among the 22 post-2008 ropes, 11 were classified as Class III and 11 as Class IV. In contrast, only 5 out of 67 ropes tested prior to 2008 were deemed non-compliant. After 2008, 11 out of 45 ropes tested fell into the non-compliant Class IV category. These results suggest that the expanded dispersion interval permitted by EN 12385-1 has contributed to an increased prevalence of ropes with inferior mechanical consistency. This trend was further corroborated by non-destructive testing conducted in mining operations, which revealed that ropes classified in Class III demonstrated significantly reduced service life compared to those in higher quality classes. For the purpose of detailed statistical analysis, representative steel ropes were selected from each of the four quality classes. All selected samples originated from mining applications and shared the same rope construction, specified in Table 1.