A unified approach for calculating the core melt frequency of a specific reactor caused by both internal and external accident initiators is demonstrated. Two classes of internal initiators are examined: transients, of which turbine trip is the chosen example, and loss‐of‐coolant events of various sizes. The concepts of hazard and fragility analysis first proposed for seismic risk analysis are linked to the frequencies of internal initiating events, and to the plant response as a function of the event intensity. Uncertainties are propagated using discrete probability distribution (DPD) arithmetic. Advantages of this approach include mathematical and conceptual consistency, and an improved uncertainty analysis, which are important considerations if risk studies are to be utilized in decision‐making based on quantitative safety