Resilience engineering understands that risks are emergent from the complexity of socio-technical systems. In this perspective, the risk assessment needs to analyze possibilities of potential risks emerging from system variabilities and interactions under hypothetical scenarios. While the Functional Resonance Analysis Method (FRAM) is a well-established method for analyzing system behavior in terms of variability, assessing relative risk levels requires more specific representation and handling of the quantitative aspects of variabilities to allow for comparative analysis and decision-making. This study proposed and examined a quantitative scheme to use FRAM for risk assessment by defining rules for variability propagation and aggregation. The proposed method represents the system more realistically with quantitative values, taking into account interactions and the adaptive operation of functions. The approach was tested via a walk-through application to an emergency response system for infectious disease. Three progressive scenarios are used in relation to managing crisis response for the 2019 coronavirus pandemic (COVID-19), and the results demonstrate the usefulness of the proposed method for assessing the relative importance of potential risks and critical conditions. Although the test example focused on a disease containment case, the proposed method can generally support strategic decision making during the governance of large-scale crisis response.