In this paper, we present an approach for quantifying the propagated uncertainty of robot systems in an online and data-driven manner. Especially in Human-Robot Collaboration, keeping track of the safety compliance during run time is essential: Misclassifying dangerous situations as safe might result in severe accidents. According to official regulations (eg, ISO standards), safety in industrial robot applications depends on critical parameters, such as the distance and relative velocity between humans and robots. However, safety can only be assured given a measure for the reliability of these parameters. While different risk detection and mitigation approaches exist in literature, a measure that can be used to evaluate safety limits online, and succinctly implies whether a situation is safe or dangerous, is missing to date. Motivated by this, we introduce a generalizable method for calculating the propagated measurement uncertainty of arbitrary parameters, that captures the accumulated uncertainty originating from sensory devices and environmental disturbances of the system. To show that our approach delivers correct results, we perform validation experiments in simulation. In addition, we employ our method in two real-world settings and demonstrate how quantifying the propagated uncertainty of critical parameters facilitates assessing safety online in Human-Robot Collaboration.