Integrating Testing and Operation-related Quantitative Evidences in Assurance Cases to Argue Safety of Data-Driven AI/ML Components

In the future, AI will increasingly find its way into systems that can potentially cause physical harm to humans. For such safety-critical systems, it must be demonstrated that their residual risk does not exceed what is acceptable. This includes, in particular, the AI components that are part of such systems' safety-related functions. Assurance cases are an intensively discussed option today for specifying a sound and comprehensive safety argument to demonstrate a system's safety. In previous work, it has been suggested to argue safety for AI components by structuring assurance cases based on two complementary risk acceptance criteria. One of these criteria is used to derive quantitative targets regarding the AI. The argumentation structures commonly proposed to show the achievement of such quantitative targets, however, focus on failure rates from statistical testing. Further important aspects are only considered in a qualitative manner -- if at all. In contrast, this paper proposes a more holistic argumentation structure for having achieved the target, namely a structure that integrates test results with runtime aspects and the impact of scope compliance and test data quality in a quantitative manner. We elaborate different argumentation options, present the underlying mathematical considerations, and discuss resulting implications for their practical application. Using the proposed argumentation structure might not only increase the integrity of assurance cases but may also allow claims on quantitative targets that would not be justifiable otherwise.