Cooperative driving with vehicle-to-everything (V2X) communication is a promising technique to improve traffic safety and efficiency. Intersection collision avoidance (ICA) is a typical safety application of it. This paper analyzes reliability of ICA with cooperative manual driving at the system level. First, the reliability of an ICA system is defined as the probability of the ICA system avoiding collisions or near-misses at intersections without failure under conditions that collisions or near-misses are about to happen. Post-encroachment time is used in the expression of this definition. Then, components of the ICA system are classified into four types: hardware, software, maneuver, and V2X communication, and a reliability block diagram (RBD) is applied to reveal how these components contribute to system reliability. Five ICA system patterns with different V2X communication modes and strategy types are compared based on RBD analysis. This shows that centralized strategies are more reliable than decentralized ones for V2I communication if software reliability of these two strategies is the same. Furthermore, reliabilities of ICA components are analyzed in detail, and they are classified into two categories based on their different impact modes on the system. Finally, a numerical example shows how to test reliability of an ICA system using reliabilities of its components by Monte Carlo simulation. Results show that closer distances from vehicles to their conflict point when alerted, longer driver reaction time, and smaller vehicle deceleration rates are more likely to lead to system failure, whereas communication latency has little effect on it.