This paper proposes a novel monitoring methodology for car-following control of automated vehicles that uses real-time measurements of spacing and velocity obtained through vehicle sensors. This study focuses on monitoring the time gap, a key parameter that dictates the desired following spacing of the controlled vehicle. The goal is to monitor deviations in actual time gap from a desired setting and detect when it deviates beyond a control limit. A random coefficient modeling is developed to systematically capture the stochastic distribution of the time gap and derive a closed-form Bayesian updating scheme for real-time inference. A control chart is then adopted to systematically set the control limits and inform when the time gap setting should be changed. Simulation experiments are performed to demonstrate the effectiveness of the proposes method for monitoring the time gap and alerting when the parameter setting needs to be changed.