Abstract: Core damage frequency/probability (CDF/CDP) is an important indicator to discuss, describe or compare the safety of nuclear power plants (NPPs). However, the concept of CDF/CDP may require to be clear to people. Generally, for the total CDP estimation purpose of multiple reactors, the damage probability of each reactor can not be accelerated directly when the reactor-year is increasing. The paper discussed the Poisson process applied in the CDP calculation. And the relationship between the CDF and CDP, and the stochastic characteristic of the core damage (CD) event should be considered intensively and cautiously in order to achieve the precise result. Results show that the simple estimation method can be valid about 2 000 reactor-years for the reactors which CDF is 1×10^－4/reactor-year, when 20 000 reactor-years for the reactors which CDF is 1×10^－5/reactor-year. Moreover, the stochastic property of CDP must be kept all along during the discussion.