Possibility-probability transformation in comparing different approaches to the treatment of epistemic uncertainties in a fault tree analysis
Résumé
Expert statements are an important source of input to risk analysis. In practice, experts might be reluctant to characterise their knowledge using precise probabilities. The theory of possibility allows for imprecision in probability assignments to be accounted for, and the possibilistic representation of epistemic uncertainty can be both combined with and transformed into a probabilistic representation. In the present paper we combine probability and possibility to represent epistemic uncertainty in a simple fault tree analysis. We apply an integrated (hybrid) probabilistic-possibilistic computational framework for the joint propagation of the epistemic uncertainty. Then we use a possibility-probability transformation and propagate the epistemic uncertainty within a purely probabilistic setting. The results of the two different approaches (hybrid and probabilistic) are compared with respect to the representation of uncertainty about the top event (limiting relative frequency) probability. Both the rationale underpinning the approaches and the computational efforts they require are examined. We conclude that the approaches relevant in a given setting depend on the purpose of the risk analysi.