Confirmation of the Validity of Central Limit Theorem in Evaluating Uncertainty of Safety System Setpoints for Nuclear Power Plants

In evaluating the uncertainty of nuclear power plant safety system setpoints, the central limit theorem(CLT) is often used when combining the uncertainties of each element. However, depending on the distribution characteristics of individual elements and the number of elements to be combined, there are cases where the central limit theorem cannot be applied. International standards are being revised to reflect this. In this paper, we describe various methodologies for calculating safety system setpoints and confirm whether the combined components follow the central limit theorem according to the distribution characteristics of the individual elements. The Monte Carlo simulation method is used as a basic tool to confirm this, and normality is verified using KS test in Python program library. Additionally, the variance characteristics of each distribution are examined and differences from the uniform distribution are analyzed. As a result of the analysis, in order for the combined component to follow the central limit theorem, if the distribution is concentrated on both sides compared to the uniform distribution, the number of input variables needs to be four or more. That is, when the number of input element uncertainty of the safety system setpoint exceeds 4, the combined uncertainty was evaluated to have normality regardless of the distribution of input element uncertainty. Therefore, it was confirmed that the method of applying CLT to calculate the coverage factor and then using it to obtain the expanded uncertainty was valid. In the case of a distribution concentrated toward the center compared to a uniform distribution, the number of variables less than 3 was required. The U type distribution, which is used to evaluate the uncertainty of wireless communication, showed characteristics closer to a uniform distribution than an inverted triangular distribution. Also, in the case of variance, it was found that the variance of the uniform distribution was larger than that of the linear distribution, confirming that this conformed to the maximum entropy principle.