This paper provides a formal approach for integrating systematically the decoupled levels 1 and 2 probabilistic safety assessment (PSA) models that are developed sequentially and differently in nature into a single PSA model for risk-informed applications (RIAs), with which the change of the level 1 events can be directly reflected in the level 2 model, and thus, the plant is able to evaluate easily the risk associated with important operational issues at the system and component levels. Its fundamental concept is the direct propagation of the level 1 core damage sequence cut sets into the level 2 model so that they are directly linked to the level 2 risk metrics [such as large early release frequency (LERF) and large late release frequency] as well as the level 2 accident sequences. Practical implementation of this approach is achieved through a sequential integration of matrix functions that would be made at successive stages for the level 2 risk calculation. Then, the final result of the integration process is given as a type of Boolean function for the level 1 core damage sequences (or cut sets) solution of each plant damage state (PDS) and PDS solution of the level 2 containment event tree sequences and the release frequencies. The plant-specific application has shown that while the present approach gives a well-formulated single operational model for RIAs, there is no essential difference with results obtained from the conventional level 2 PSA approach that directly uses the numerical results of the level 1 core damage sequences to obtain the level 2 risk metrics.