This paper presents a reliability analysis method for automated vehicles equipped with adaptive cruise control (ACC) and autonomous emergency braking (AEB) systems to avoid collision with an obstacle in front of the vehicle. The proposed approach consists of two main elements, namely uncertainty modeling of traffic conditions and model-based reliability analysis. In the uncertainty modeling step, a recently developed Gaussian mixture copula method is employed to accurately represent the uncertainty in the road traffic conditions using the real-world data, and to capture the complicated correlations between different variables. Based on the uncertainty modeling of traffic conditions, an adaptive Kriging surrogate modeling method with an active learning function is then used to efficiently and accurately evaluate the collision-avoidance reliability of an automated vehicle. The application of the proposed method to the Department of Transportation Safety Pilot Model Deployment database and an in-house built Advanced Driver Assist Systems with ACC and AEB controllers demonstrate the effectiveness of the proposed method in evaluating the collision-avoidance reliability.