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• AV disengagement on public roads dominated by causes due to a planning issue. • AV disengagement induced by lacking certain numbers of radar and LiDAR sensors. • Drivers' take-over time impacted by disengagement cause and roadway characteristics. • To improve AV disengagements five or more radar sensors are needed. • Optimal number of LiDAR sensors to be installed is 3 or 4. Automated vehicles (AV) testing on the public roads is ongoing in several states in the US as well as in Europe and Asia. As long as the automated vehicle technology has not achieved full automation (Level 5), human drivers are still expected to take over the steering wheel and throttles when there is an automated vehicle disengagement. However, contributing factors and the mechanism about automated vehicle-initiated disengagement has not been quantitatively and comprehensively explored and investigated due to the lack of field test data. Besides, understanding human drivers' perception and promptness of reaction to the AV disengagement is essential to ensure safety transition between automated and manual driving. By harnessing California's Autonomous Vehicle Disengagement Report Database, which includes the AV disengagement data from field tests in 2016–2017, this paper quantitatively investigated the AV disengagement using multiple statistical modeling approaches that involve statistical modeling and classification tree. Specifically, the paper identifies the contributing factors impacting human drivers' promptness to AV disengagements, and quantitatively investigates the underlying causes to AV disengagements. Results indicate that current AV disengagement on public roads is dominated by causes due to a planning issue. The cause of an AV disengagement is significantly induced by lacking certain numbers of radar and LiDAR sensors installed on the automated vehicles. These thresholds of these sensors needed are revealed. Cause of disengagement and roadway characteristics significantly impact drivers' take-over time when facing an AV disengagement. AV perception or control issue-based disengagement can significantly extend drivers' perception-reaction time to take over the driving. The quantitative knowledge obtained ultimately facilitates revealing the mechanisms of the automated vehicle disengagements to ensure safe AV operations on public roads. [ABSTRACT FROM AUTHOR]