Comparison of state-of-knowledge correlation effect associated with lognormal, beta, and gamma uncertainty distributions

Abstract

In the probabilistic safety assessment (PSA) of nuclear power plants, the state-of-knowledge correlation (SOKC) is required to be considered when estimating the risk measures and their uncertainties. Specifically, the SOKC must be taken into account when the failure data for similar components are aggregated to produce the failure rate or failure probability for the components and their uncertainty distributions. The objective of this study is to mathematically prove what has been numerically observed in the existing studies: The SOKC effect is more significant if the uncertainty is modeled with a lognormal distribution than when it is modeled with a gamma or beta distribution when the parameters of the two distributions are estimated from the same failure data by using the method of moments. An example based on the frequency calculation for interfacing system loss of coolant accidents is provided to demonstrate the proof. The mathematical proof provides a relationship between the raw moments of lognormal, gamma, and beta distributions, which is expected to be valuable in probability and statistics theories.