Risk assessment of uncertain random system—Level-1 and level-2 joint propagation of uncertainty and probability in fault tree analysis

Uncertainty analysis plays a significant role in risk assessment, which consists of two tasks: uncertainty expressions of input variables in the model and their propagations through the model built. We aim to provide, in fault tree analysis context, suitable methods of expression and propagation of uncertainty corresponding to different stages of knowledge that the risk analyst own, where frequentist probability is used to express the aleatory uncertainty and uncertainty theory is used to represent the epistemic uncertainty. To do so, we divide the analyst's knowledge state into five different stages, and develop the correct expression of uncertainty corresponding to each stage, where different combinations of probability and uncertainty are considered. Methods of propagation of these uncertainties through fault trees are further developed, where we introduce probability distributions, uncertainty distributions, newly-developed level-2 distributions, and the varying time t into the operational law for Boolean uncertain random system to better address the needs of practical risk assessments. A case study is conducted to show the differences in the propagation methods corresponding to various knowledge stages, and the results highlight that the proposed methods are effective and could deliver clear messages to decision makers.