Fully autonomous vehicles (AVs), i.e., AVs with autonomy level 5, are expected to dominate road transportation in the near-future and contribute trillions of dollars to the global economy. The general public, government organizations, and manufacturers all have significant concern regarding resiliency and safety standards of the autonomous driving system (ADS) of AVs . In this work, we proposed and developed (a) `Kayotee' - a fault injection-based tool to systematically inject faults into software and hardware components of the ADS to assess the safety and reliability of AVs to faults and errors, and (b) an ontology model to characterize errors and safety violations impacting reliability and safety of AVs. Kayotee is capable of characterizing fault propagation and resiliency at different levels - (a) hardware, (b) software, (c) vehicle dynamics, and (d) traffic resilience. We used Kayotee to study a proprietary ADS technology built by Nvidia corporation and are currently applying Kayotee to other open-source ADS systems.