Advances in communications and sensing technology have enabled the development of cooperative ITS technologies such as connected and automated vehicle (CAV) applications including adaptive cruise control (ACC) and cooperative adaptive cruise control (CACC) that could perform driving tasks with little human feedback. However, there are some key concerns and knowledge gaps regarding the impact of delay in communicated messages on CAV platoon safety and stability. This study contributes by analyzing the impact of delay while controlling for other factors on CAV platoon safety and stability using the concept of driving volatility. Real-world experimental data from a field test were used to examine the lead vehicle (LV) and following vehicles (FVs) behavior in a five-vehicle platoon with multiple scenarios by developing switching regime models. Results show that CACC reduces volatility in both LV and FVs compared to ACC system which can be attributed to the vehicular communication and motion synchronization of CACC. However, delay is observed to increase the likelihood of volatility and contribute to instability of platoons. FVs have more volatile behavior as compared to LV since the instability is transmitted through the string of the platoon. Further, Bayesian model reveals that a unit increase in delay is observed to increase the collision risk by 4%. Other confounding factors such as disengagement and ACC override contribute to higher volatility of platoon while the likelihood of high volatility in both LV and FVs decreases with increases in gap to the preceding vehicle. The risk of collision is expected to increase by 6.2% in response to a unit increase in disengagements. Likewise, ACC override increases the risk of collisions by 5.4%. These results have practical implications for considering delays in CAV performance analysis and for designing robust CACC algorithms with minimum delays in the future.