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Autonomous driving systems must guarantee safety, which requires strict real-time performance. A series of processes, from sensor data input to vehicle control command output, must be completed by the end-to-end deadline. If a deadline miss occurs, the system must quickly transition to a safe state. To improve safety, an early detection method for deadline misses was proposed. The proposed method represents the autonomous driving system as a directed acyclic graph (DAG) with a mixture of timer-driven and event-driven nodes. It assigns appropriate time constraints for each node based on the end-to-end deadline. However, the existing methods assume the worst-case execution time (WCET) for calculating the time constraints of each node and do not consider the execution time variation of nodes, making the detection of deadline misses pessimistic. This paper proposes a deadline miss early detection method to determine the possibility of deadline misses quantitatively at the beginning of each node execution in a DAG task. It calculates the time constraints of each node using probabilistic execution time, which treats execution time as a random variable. Experimental evaluation shows that the proposed method reduces pessimism, which is a problem of conventional methods using WCET, and then achieves more accurate early detection of deadline misses. The evaluation also indicates that the execution time of static analysis required for deadline miss early detection is within a practical level.