## 3 Proposed Credibility Evaluation Methodology
The correlation index measures the similarity between real-world and XILS tests at the parameter level, reflecting the accuracy of the simulation component models with reference to the respective parameters. The parameter-based reliability (\(R_{m}\)) is then evaluated based on whether these two indices meet their defined evaluation criteria. Figure 2: Overall process flow of proposed methodology for evaluating XILS credibility. Scenario-based reliability assessment involves calculating the applicability index (\(A_{k}\)) and correlation index (\(C_{k}\)) for each scenario. The scenario applicability index quantifies how consistently XILS test results align with real-world test results in a given scenario, while the scenario correlation index measures the overall similarity between real-world and XILS tests at the scenario level. The scenario-based reliability (\(R_{k}\)) is then determined based on whether these two indices meet their predefined evaluation criteria. Dynamics-based fidelity assessment involves calculating the dynamic correlation index (\(D_{k}\)) centered on the vehicle's six-degree-of-freedom (6 DOF) motion characteristics. This index measures the similarity between real-world tests and XILS tests based on information on the vehicle's three types of translational movements and three types of rotational movements. The dynamics-based fidelity (\(F_{k}\)) is then evaluated based on whether \(D_{k}\) meets the defined evaluation criterion. When the parameter-based reliability (\(R_{m}\)), scenario-based reliability (\(R_{k}\)), and dynamics-based fidelity (\(F_{k}\)) have all been validly assessed, the XILS platform is deemed credible. This multi-dimensional approach minimizes the potential biases arising from single-perspective evaluations and comprehensively verifies the credibility of the XILS platform for ADS validation. We employed the comparative analysis techniques proposed by [PERSON] [31] to measure the similarity between the datasets from the real-world and XILS tests. [PERSON] [31] proposed a comprehensive similarity evaluation metric that combines the correlation coefficient (\(f_{1}\)) for integrated comparison, the Zilliacus error (\(f_{2}\)) for point-to-point comparison, and the Geers metric (\(f_{3}\)) to analyze magnitude and phase errors separately. The correlation coefficient (\(f_{1}\)) is defined by Equation (1), where \(y_{1}\) and \(y_{2}\) represent the two datasets to be compared, and \(\omega\) denotes the number of sample data points, with each data point indexed by \(i\) from 0 to \(\omega\)[32]. The correlation coefficient ranges from \(-1\) to 1, where values closer to 1 indicate stronger positive linear relationships between the dataset trends. The Zilliacus error (\(f_{2}\)) is calculated using Equation (2), which normalizes the sum of absolute point-wise errors \(|y_{1,i}-y_{2,i}|\) by the sum of absolute values of the reference dataset; lower \(f_{2}\) values indicate better point-to-point agreement between the two datasets [33]. The Geers metric (\(f_{3}\)) is calculated as the square root of the sum of the squares of the magnitude error (\(M_{G}\)) and phase error (\(P_{G}\)), as expressed in Equation (3). The magnitude error \(M_{G}\) in Equation (4) quantifies the energy ratio between datasets through their squared sums, while the phase error \(P_{G}\) in Equation (5) measures temporal alignment differences using normalized cross-correlation [34]. This technique enables separate evaluations of amplitude differences and temporal synchronization between the datasets. Finally, the combined similarity metric (\(y_{R}\)) is calculated as the weighted sum of these three indicators, as shown in Equation (6). Here, \(\eta_{1}\), \(\eta_{2}\), and \(\eta_{3}\) represent the weighting factors for the three metrics, which can be adjusted according to their respective importance levels. In this study, equal weighting (\(\eta_{1}=\eta_{2}=\eta_{3}=1/3\)) was applied to ensure balanced consideration of all three similarity aspects.