In the process of simplifying the complex fate of the plant into a binary state, the information loss is inevitable. To minimize the information loss, the quantification of plant safety status has been formulated through the combination of the probability density function arising from the sensor measurement and the membership function representing the expectation of the state of the system. Therefore, in this context, the safety index is introduced in an attempt to quantify the plant status from the perspective of safety. The combination of probability density function and membership function is achieved through the integration of the fuzzy intersection of the two functions, and it often is not a simple task to integrate the fuzzy intersection due to the complexity that is the result of the fuzzy intersection. Therefore, a methodology based on the Algebra of Logic is used to express the fuzzy intersection and the fuzzy union of the arbitrary functions analytically. These exact analytical expressions are then numerically integrated by the application of Monte Carlo method. The benchmark tests for rectangular area and both fuzzy intersection and union of two normal distribution functions have been performed. Lastly, the safety index was determined for the Core Reactivity Control of Yonggwang 3&4 using the presented methodology.