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The lack of data due to the high cost of experiments, limited knowledge of system structure, and coupling failure mechanism make it necessary to consider uncertainties when analyzing the reliability of complex systems. This paper provides a comprehensive work for system reliability analysis under consideration of mixed uncertainties. First, Bayesian networks (BNs) are used to model the structure of complex systems. Second, mixed uncertainties are described via a probability box and accurately quantified by the Bhattacharyya distance, which can synthetically represent the mean and variance of two data sets. Then, the importance of components with mixed uncertainties is defined and analyzed. Finally, a comprehensive sensitivity index is proposed for sensitivity analysis and epistemic uncertainty tracing of data sources based on the Bhattacharyya distance. This method is used to analyze the reliability of an auxiliary power supply system of a train and verifies the feasibility and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]