This work aims to investigate the effect of driver response to relayed messages through Human Machine Interface (HMI) on the effectiveness of Human-Vehicle Interface (HVI) and to enable the optimized design of HMI. The investigation and mathematical modeling cover vehicles with Advanced Vehicle Assistant System (ADAS), which operates using Advanced Vehicle Control System (AVCS). The presented model uses driver response time and machine (electronics, sensors, processors) processing time to measure vehicular efficiency and driver interaction, which is also a function of the HMI design, and the way messages are passed to the driver. The produced model uses a probability function that can be used in the design and testing process to assess the effect of failure on the designed interface and relates the function to the driver's response time ratio and the vehicle electronics' processing time. The presented work concluded that as the driver response time increases, effective interaction decreases as a probability function. Also, as the driver response time deviates from the specified threshold, the effective interaction decreases, which also applies to the processing time. In addition, as the time ratio between the driver responses to the machine processing (Time Ratio) increases, the effective interaction parameter (R) value decreases. The work also proved that a more adaptive model is possible using a probability function correlated to the response time ratio to processing time.