Handling parameter and model uncertainties by continuous gates in fault tree analyses

Fault tree analyses are widely used in probabilistic risk assessments (PRA) to model and evaluate safety system reliability. Coherent results can then be obtained by expressing probabilities according to input information. However, if uncertainties in parameters (e.g. failure rates) and models (e.g. relationships between events) lead to high uncertainty in results, the latter may not be robust enough to be helpful. It is therefore necessary to perform uncertainty analyses and, in order to handle both parameter and model uncertainties in a fault tree framework, a continuous gate denoted the ‘C-gate’ is proposed. By acting on ‘weights’, it is then allowed to continuously graduate model part structures between parallel and series. C-gates can also be translated into equivalent fault trees, using fictitious events, so that classical reliability tools are used to perform reliability evaluations with both parameter (failure rates) and model (through the weights) uncertainty analyses. An application on a new technology-based transmitter shows that results can be obtained with relatively low uncertainty and, in some cases, even with lower variances than any of the inputs. These properties are discussed and tend to demonstrate that the lack of knowledge on the structures of some parts of the model can be handled and partially compensated for by the proposed fault tree approach to perform PRA.