System of interest (SoI) failures can sometimes be traced to an unexpected behavior occurring within another system that is a member of the system of systems (SoS) with the SoI. This article presents a method for use when designing an SoI that helps to analyze an SoS for unexpected behaviors from existing SoS members during the SoI's conceptual functional modeling phase of system architecture. The concept of irrationality initiators—unanticipated or unexpected failure flows emitted from one system that adversely impact an SoI, which appear to be impossible or irrational to engineers developing the new system—is introduced and implemented in a quantitative risk analysis method. The method is implemented in the failure flow identification and propagation framework to yield a probability distribution of failure paths through an SoI in the SoS. An example of a network of autonomous vehicles operating in a partially denied environment is presented to demonstrate the method. The method presented in this paper allows practitioners to more easily identify potential failure paths and prioritize fixing vulnerabilities in an SoI during functional modeling when significant changes can still be made with minimal impact to cost and schedule.