A study on updating belief functions for parameter uncertainty representation in Nuclear Probabilistic Risk Assessment

Abstract : Probabilistic Risk Assessments (PRA) are used to achieve a safe design and operation of Nuclear Power Plants. The impact of uncertainties which may affect PRA results must thus be taken into account in the decision making process. These uncertainties due to the lack of data have been recently seen as mainly epistemic ones and it has been recommended to characterize them by the belief functions of Dempster-Shafer Theory rather than a presumed single probability distribution. The current construction of these functions is based on the data provided by PRA data handbooks using traditional statistical tools like Maximum Likelihood Estimation (MLE). However, this approach is only appropriate when data coming from the operating feedback observations are sufficiently large as required in the MLE approach. Furthermore, when wishing to incorporate other sources of information, such as expert's opinions, the pooling data of MLE has limits to account for these kinds of information. Therefore, in order to overcome this problem, two alternative perspectives based on the Dempster's rule of combination and the Generalized Bayesian Theorem for constructing and updating the belief functions in a more effective way will be presented in this paper. These two approaches will be studied for the use in the context of PRA. The comparison of these two approaches with the current method is carried out through a practical example. Some conclusions about the application of these approaches will be drawn.