## 3 Case Study: Structural Factor Analysis for Public Transportation Bus
### Selection of Critical Structural Factors
#### 3.4.1 Factor Selection Considering Occurrence Probability by Fault Tree Analysis  
In order to assess the occurrence probability of each factor contributing to vehicle malfunctions, FTA enables the establishment of a theoretical relationship between vehicle safety problems (TE), critical systems (Immediate Events), and the failure-causing factors (BEs). The descriptions of Immediate Events (IEs) and BEs are provided in Table S27. Figure S1 shows the constructed fault tree diagram for analyzing failure-causing factors. The occurrence proportion of BEs is extracted from the maintenance data collected. Due to confidentiality constraints, the specific details of the maintenance records cannot be fully disclosed. Utilizing the BIM method presented in Section 2.3, the impact of each BE on the occurrence of the TE is assessed. Table S28 illustrates the identification and ranking of the BEs based on their criticality concerning TE occurrence. 4.2 Factor Selection Considering Severity Impact by Interval-Valued Pythagorean Fuzzy Analytic Hierarchy Process  
Considering the impact of the fault severity, the factors identified in Section 3.2 are ranked by IVPF-AHP, as introduced in Section 2.4. The structure of the IVPF-AHP analysis for vehicle operation safety is consistent with the FTA structure. A BE is treated as the factor used for IVPF-AHP analysis. This study consults the DMs using a questionnaire-form survey to obtain the pairwise evaluation for factors. The DMs use the 10-point linguistic rating scale, as shown in Table 1, to compare and score the relative influence between the factor pairs. The linguistic data are obtained from each expert's assessment. The maximum linguistic rating value of the corresponding criterion is selected to generate the final initial direct relation matrix. Finally, the initial direct relation matrix achieves consensus at the brainstorming meeting. The initial pairwise comparative matrices received from the expert team are given in the Supplementary Materials. The pairwise comparative matrices can be established as shown in Tables S1-S20 to assess each factor's relative severity impact degree. The consistency examinations for pairwise comparison matrices received from experts are conducted. Since all the CR values are smaller than 0.1, it is evident that pairwise comparison matrices are logically consistent and trustworthy. The calculation results are summarized in Table S21. 3.4.3. Factor Selection Considering Both Occurrence Probability and Severity Impact  
To adjust the ranking of factors taking both fault severity and fault occurrence probability into consideration simultaneously, the combination ranking values of factors are calculated as in Equation (25). After consulting the expert team, the adjustment weight \(w\) is set as 0.3. The modified ranking results are presented in Table S29. This paper selects the more critical ones to reduce the dimension of the factor set and simply uses the DEMATEL analysis complexity. The top 30 out of 62 factors are selected for further evaluation in DEMATEL, and the list of these critical factors is presented in Table 4. The critical factors selected are confirmed by experts in meetings, and the selection results are consistent with the domain knowledge. 4.4 Cause-Effect Relationship Analysis by Interval-Valued Pythagorean Fuzzy Decision-Making Trial and Evaluation Laboratory  
The expert team is invited to score the relative importance of 30 critical factors using a questionnaire-form survey. Experts use the five-point linguistic rating scale, as shown