## 4 Case Study
### Weight Calculation  
To ensure the professionalism and reliability of the evaluation results when determining subjective weights using the G1 method and scoring subjective risk factors, experts were invited from multiple channels, including universities, research institutions, and field operations. Ultimately, an evaluation team of nine experienced individuals was assembled, comprising scholars, technical specialists, and on-site experts. The team included two experts with senior professional titles from leading universities in the field of railway engineering, both of whom have extensive experience in track safety research. Additionally, three experts held deputy senior professional titles, specializing in the R&D of railway track maintenance technologies. The team also included four on-site technical experts with senior engineer titles, each with over 10 years of experience in track maintenance management and all of whom had actively participated in maintenance operations on the Lanzhou-Xinjiang Railway. Using the five track maintenance operations listed in Table 4 as examples, the expert team assessed the subjective risk factors by combining first-hand operational knowledge, professional experience, and relevant industry standards. The resulting expert scores and assigned values are listed in Table 5.  
Subjective weight determination: The subjective weights of the indices were calculated following the G1 method steps outlined in Section 2.1. For example, to calculate the subjective weights of \(B_{1}-B_{4}\), they were ranked based on their relative importance in influencing the risk of track maintenance operations, resulting in the following order \(B_{1}>B_{4}>B_{2}>B_{3}\), i.e., \(E_{1}^{*}(B_{1})>E_{2}^{*}(B_{4})>E_{3}^{*}(B_{2})>E_{4}^{*}(B_{3})\). The quantified values of the relative importance between adjacent indices, obtained through expert assessment, were 1.3, 1.4, and 1.2, respectively. Based on these values, the weights were computed using Equations (1) and (2). Table 6 presents the ranking and quantified degree of importance for the first-level indices of track maintenance operations as provided by the expert panel. Following the same procedure, the subjective weights of the second-level indices were also calculated using the G1 method, with the results shown in Table 7. \begin{table}
\begin{tabular}{c c c} \hline \begin{tabular}{c} **First-Level Index** \\ **Sequence** \\ \end{tabular} & \begin{tabular}{c} **Quantification of the** \\ **Importance Degree of** \\ **First-Level Indexes** \\ \end{tabular} & \begin{tabular}{c} **Second-Level Index Sequence** \\ **Second-Level Indexes** \\ \end{tabular} & \begin{tabular}{c} **Quantification of the** \\ **Importance Degree of** \\ **Second-Level Indexes** \\ \end{tabular} \\ \hline \begin{tabular}{c} \(B_{1}>B_{4}>B_{2}>B_{3}\) \\ \end{tabular} & 1.3, 1.4, 1.2 & \
\begin{tabular}{c} \(B_{12}>B_{14}>B_{13}>B_{11}\) \\ \(B_{21}>B_{22}\) \\ \(B_{31}>B_{32}>B_{35}>B_{33}>B_{34}\) \\ \(B_{13}>B_{11}>B_{12}>B_{14}\) \\ \end{tabular} &
\begin{tabular}{c} 1.4, 1.3, 1.1 \\ 1.3 \\ 1.3 \\ 1.2, 1.6, 1.2, 1.1 \\ 1.3, 1.1, 1.2 \\ \end{tabular} \\ \hline \end{tabular}
\end{table} 
Table 6: Quantification of the sequence and degree of importance of risk assessment indices.