When dealing with modern complex systems, the relationship existing between components can lead to the appearance of various dependencies between component failures, where multiple items of the system fail simultaneously in unpredictable fashions. These probabilistic common cause failures affect greatly the performance of these critical systems. In this paper a novel methodology is developed to quantify the importance of common cause failures when hybrid uncertainties are presented in systems. First, the probabilistic common cause failures are modeled with Bayesian networks and are incorporated into the system exploiting the α factor model. Then, probability-boxes (bound analysis method) are introduced to model the hybrid uncertainties and quantify the effect of uncertainties on system reliability. Furthermore, an extended Birnbaum importance measure is defined to identify the critical common cause failure events and coupling impact factors when uncertainties are expressed by probability-boxes. Finally, the effectiveness of the method is demonstrated through a numerical example