Objective: As a crucial component of power systems, the valve hall plays a vital role in ensuring the safe and stable operation of converter stations, as well as the reliable transmission of electricity. However, earthquakes pose a significant threat to the integrity and functionality of these systems. Under seismic loading, due to the uniformity of the ground motion input and the mechanical and functional coupling between components, the dynamic responses of the equipment are correlated. This interdependence challenges the conventional assumption of independent component failures, highlighting the need for more advanced reliability modeling. Methods: To demonstrate the importance of considering response correlation between components, this study first analyzes the reliability of series and parallel systems under two extreme conditions: complete independence and complete correlation. The findings show that the correlation between equipment responses has a significant effect on system reliability, especially when the number of components increases or the failure probability varies widely. To quantify the correlations within the valve hall system, finite element simulations were conducted on both high-voltage and low-voltage valve halls of a ±800 kV converter station. The seismic responses of individual equipment were obtained under various ground motion inputs. Based on these data, a Gaussian copula-based method was employed to model the joint behavior of equipment responses. This method captures their statistical dependencies without assuming a predefined joint distribution. The analysis process mainly consists of marginal distribution modeling of the responses, transformation to uniform and normal distributions, determination of the correlation matrix, generation of independent normal samples, singular value decomposition of the correlation matrix, standard normal transformation, inverse mapping to the uniform domain, and generation of correlated samples. This approach enables the construction of a realistic joint distribution of equipment responses while preserving their marginal characteristics. Using the correlated samples generated through the Gaussian copula method, the system-level reliability of the valve hall was evaluated while accounting for dependent failure behavior. Results: The Gaussian copula method effectively modeled the correlation structure of variables using the correlation matrix, enabling accurate modeling of the correlation structure of the response states of the whole system. The assumption of complete independence of component states underestimated the actual system reliability. The degree of underestimation varied significantly with the peak ground acceleration (PGA), with the most pronounced effect observed at PGA=0.400g. Furthermore, neglecting the correlation between component failures resulted in an overestimation of the economic losses of the converter station, and the magnitude of this overestimation increased with the system's design life. Conclusions: The proposed reliability assessment framework incorporates equipment response correlations, yielding more accurate and realistic assessments of valve hall system performance under seismic conditions. This method also overcomes the limitations of traditional approaches based on independent assumptions, which are commonly adopted in large-scale system reliability analysis due to their computational simplicity. The proposed method is flexible and extensible, with broad application prospects in the reliability and risk assessment of complex infrastructure systems subjected to extreme events.