The global electric and hybrid aircraft market utilizing lithium-ion Energy Storage Systems (ESS) as a means of propulsion, is experiencing a period of extraordinary growth. We are witnessing the development of some of the most cutting-edge technology, and with that, some of the most complex challenges that we as an industry have ever faced. The primary challenge, and the most critical cause of concern, is a phenomenon known as a “Thermal Runaway”, in which the lithium-ion cell enters an uncontrollable, self-heating state, that if not contained, can propagate into a catastrophic fire in the aircraft. A Thermal Runaway (TR) can be caused by internal defects, damage, and/or abuse caused by an exceedance of its operational specifications, and it is a chemical reaction that cannot be stopped once the cell has reached its trigger temperature. There are many technical papers that explore the characteristics of battery cells and the TR as a failure mode, but the failure mechanism(s) are still not clear. In addition, there have been several publicized incidents of TR that has added pressure to the already steep challenge of how to quantify these failures without extensive data – since the emergence of ESS as a means for propulsion, being still relatively new. When there is not enough confidence in the data collection and analysis for these failure modes, the question remains to how we can perform a robust system safety assessment. This paper will help the reader to understand some of the characteristics of a Thermal Runaway and propose an adapted ARP-based approach for conducting the system safety assessment of an ESS, utilizing both qualitative and quantitative ARP 4761 methods.