Advanced probabilistic risk assessment through continuous fault trees using R-functions

The current state-of-the-art in traditional, Level 1 probabilistic risk assessment (PRA) is the analysis of fault and event trees based on Boolean algebra and cut sets. This approach allows for the delineation of the response of a system to different initiating events and calculating the probability of the failure of a system under different scenarios. Despite its impressive success in the past, classical binary PRA has inherent and fundamental limitations. These limitations include the binary and deterministic nature of the traditional PRA framework, which limits the capability to model risk scenarios with partial (partially open valve), incomplete (wall thinning), and poorly understood (pump loss of power) failures. In addition, discovering the risk scenarios and optimization of the reliability of a system is difficult in the binary PRA framework. Addressing these limitations can significantly improve the quality, reliability, acceptability, and credibility of the PRA. This paper focuses on establishing the proof of principle that mathematically rigorous methodology can be developed that uses continuous fault trees, instead of binary choices. The proposed novel methodology is based on the theory of R-functions. Having converted the Boolean tree into an analytical function, it will now be possible to analyse this function in a continuous domain and apply all available analytical tools, including differentiation and integration, to study the properties of the function and optimize it with respect to the total probability of the system'.