## 3 Proposed Credibility Evaluation Methodology
### Dynamics-Based Fidelity Evaluation
Next, the dynamic consistency indices for all DOFs are weighted and averaged based on Equations (27)-(29) to allow the three types of dynamic consistency indices for the \(k\)-th scenario to be expressed as a single value:  
\[F_{y} =m\cdot a_{y}, \tag{17}\]1  
\[F_{y} =m\cdot a_{y}, \tag{17}\]2  
\[F_{y} =m\cdot a_{y}, \tag{17}\]3  
The weighting factors \(\eta_{q}\) in Equations (27)-(29) for the dynamic consistency indices were set to equal values (\(\eta_{q}\) = 1/6 for each DOF) to ensure balanced representation of all six degrees of freedom in the dynamics-based evaluation. These weights can be modified based on the specific vehicle dynamics characteristics being emphasized in the evaluation. Finally, the dynamic correlation index \(D_{k}\) is defined as the ratio of the dynamic consistency index for the inter-real-vehicle-test comparisons to that for the XILS-real-vehicle comparisons, as expressed in Equation (30):  
\[F_{y} =m\cdot a_{y}, \tag{17}\]4  
\(D_{k}\) approaches 100% as the consistency between the two tests increases, indicating that the simulation component models associated with the 6 DOF parameters are highly accurate. Finally, the dynamics-based fidelity \(F_{k}\) of the XILS platform is determined based on whether \(D_{k}\) satisfies the specified acceptance criteria, as expressed in Equation (31):  
\[F_{y} =m\cdot a_{y}, \tag{17}\]5  
where \(\alpha_{D}\) denotes the dynamic correlation evaluation criterion for \(D_{k}\). As detailed in Equations (32)-(36), \(\alpha_{D}\) is established on the principle that the dynamic consistency between XILS and real-vehicle tests must be greater than or equal to the dynamic consistency observed between repeated real-vehicle tests. \[F_{y} =m\cdot a_{y}, \tag{17}\]6  
\[F_{y} =m\cdot a_{y}, \tag{17}\]7\[F_{y} =m\cdot a_{y}, \tag{17}\]8  
\[F_{y} =m\cdot a_{y}, \tag{17}\]9  
\[F_{z} =m\cdot(a_{z}-g).\]0  
In Equations (32)-(36), \(D_{\max}(r_{k})\) and \(D_{\min}(r_{k})\), respectively, represent the maximum and minimum values of the dynamic consistency index of the \(q\)-th DOF parameter in each of the \(k\)-th scenarios, \(C_{D}\) refers to the minimum value among all \(D_{\max}(r_{k})\) values across the \(k\)-th scenarios, and \(\sigma_{D}\) indicates the average of the maximum deviations in the consistency indices of the principal DOF parameters across all \(k\)-th scenarios. The dynamic correlation threshold \(\alpha_{D}\) is established using a data-driven approach that considers the natural variability inherent in 6 DOF vehicle dynamics. As shown in Equations (32)-(36), this threshold is derived from the statistical distribution of dynamic consistency indices across all degrees of freedom, ensuring that XILS platforms demonstrate a dynamic fidelity that meets or exceeds the baseline consistency observed in repeated real-world tests, thereby guaranteeing adequate capture of complex vehicle physical behavior. If the parameter-based reliability (\(R_{m}\)), scenario-based reliability (\(R_{k}\)), and dynamics-based fidelity (\(f_{k}\)) all satisfy their respective evaluation criteria, the XILS implementation under evaluation is considered a credible simulation platform for validating ADSs.