## 3 Problem Formulation  
The relationship between the mechanical properties of individual wires and the operational lifespan of steel ropes has gained increasing recognition through empirical observations. This includes non-destructive testing during service and tensile testing carried out before rope installation. However, existing theoretical models that describe the mechanical behavior of steel ropes under tensile and bending loads often fail to account for the variability in the strength class of the wires that comprise the rope [17]. Empirical observations from real-world operations have highlighted the critical importance of input material quality, specifically, the uniformity of wire strength within each rope. Historically, this issue was addressed by the now obsolete DIN 21 254 standard for mining ropes, which, in Article 4.1.3, specified that the maximum allowable dispersion of wire strength class should be within \(\pm\)10% of the mean strength value of all tested wires. A similar requirement was adopted by the former Slovak standard STN 02 4301 [18; 19]. [PERSON] et al. [20] further contributed to this topic by introducing a classification system for steel ropes based on empirical findings from long-term operational monitoring. Their work underscores the importance of wire strength uniformity as a key determinant of rope quality and reliability. To classify steel ropes into three quality categories, the method originally proposed by [PERSON] et al. [21] involves comparing the mean strength of all tested wires to the average of a subset of wires whose strength values fall below that mean. This model provides a practical tool for evaluating the internal consistency and mechanical quality of wires within a rope. Subsequent studies by [PERSON] et al. [21] and [PERSON] et al. [22] expanded this framework and applied it to ropes used in the Slovak mining industry. Their analyses further confirmed that consistency in wire strength is crucial to overall rope reliability. In contrast, currently valid European standards, specifically the EN 12385 series, do not mandate strict tolerances for wire strength class dispersion in finished ropes. On the contrary, EN 12385-1,Annex B, paragraph B.3.1.1, defines the allowable strength class tolerance for new wires (prior to incorporation into the rope) within the range of <0%, +15%>. Furthermore, paragraph B.3.3 of the same annex permits a post-weaving strength class deviation of \(-50\) MPa to +15 MPa for wires extracted from a finished rope. This standard essentially acknowledges a potential reduction in wire strength due to deformation and stress introduced during the rope weaving process [16]. However, such a broad permissible interval may allow manufacturers to incorporate wires of varying strength classes into a single rope, potentially undermining overall rope reliability. Laboratory analyses conducted as part of this study confirmed the inadequacy of the tolerances prescribed in Annex B.3.3 of EN 12385-1 for evaluating ropes used in demanding applications. Extensive testing of mining ropes from multiple manufacturers revealed that some producers continue to adhere to stricter quality standards--specifically, by maintaining a narrow dispersion interval for wire strength class--thereby preserving the mechanical integrity and consistency of their rope products [16]. In an ideal scenario, all wires within a steel rope would belong to the same strength class, ensuring maximum uniformity and predictable mechanical performance. However, such uniformity is not practically attainable due to inherent material and manufacturing variations. The closest approximation to this ideal can be achieved through the careful and targeted selection of input wire materials used in the construction of rope strands. Given the mechanical impracticality of achieving absolute uniformity, our investigation focused on analyzing the dispersion of wire strength classes based on real-world rope samples that exhibited the narrowest observed strength intervals.