•The common cause failures is modeled and quantified by decomposed partial α factors;•Mixed uncertainties are quantified and expressed by the D-S evidence theory;•A hierarchical structure of system reliability is constructed by adding decomposed CCF events layer in evidential network;•Importance and imprecise sensitivities analysis methods are extended and developed;•The proposed method is effectively used to analyze the reliability of an auxiliary power supply system of a train. Redundant design has been widely used in aerospace systems, nuclear systems, etc. which calls for particular attention to common cause failure problems in such systems with various kinds of redundant mechanisms. Besides, imprecision and epistemic uncertainties also need to be taken into account for system reliability modeling and assessment. In this paper, a comprehensive study based on the evidential network is performed for the reliability analysis of complex systems with common cause failures and mixed uncertainties. The decomposed partial α-factor is used to separate the contribution of independent parts and common cause parts of basic failure events. Mixed uncertainties are quantified and expressed by the D-S evidence theory, and the system reliability with uncertainties is modeled by evidential network. Furthermore, two layers, i.e. a decomposed event layer and coupling layer, are embedded into the evidential network of the system, and, as a result, the hierarchical structure of system reliability is constructed. The importance and sensitivities of various component types and their impact on system reliability are detected. The presented evidential network-based hierarchical method is applied to analyze the reliability of an auxiliary power supply system of a train and the results demonstrate the effectiveness of this method.