Traditionally, the safety of a nuclear reactor system has been assessed through a set of mechanistic calculations of bounding accident sequences using conservative models. Extensive experience in the operation and analysis of nuclear reactor systems has led to two complementary approaches: best-estimate mechanistic calculations with a quantitative estimate of the uncertainty for assessing conformance with acceptance criteria based on technical limits and probabilistic risk analysis of the event sequences due to the probability of failure of safety systems. Both assess the safety of the reactor system; however, the emphasis, especially in the estimation of probabilities, is different in the two approaches. Yet both address the same concern: the safety of the reactor system. We discuss the formal relations that are necessary for a risk-consistent analysis of the safety of the nuclear reactor systems with respect to the two current approaches.