Probability and possibility based representations of uncertainty in fault tree analysis

Enrico Zio (1) , Terje Aven (2) , Piero Baraldi (3) , R. Flage (2)

1 SSEC - Chaire Sciences des Systèmes et Défis Energétiques EDF/ECP/Supélec
2 University of Stavanger
3 Dipartimento di Energia [Milano]

Expert knowledge is an important source of input to risk analysis. In practice, experts might be reluctant to characterize their knowledge and the related (epistemic) uncertainty, using precise probabilities. The theory of possibility allows for imprecision in probability assignments. The associated possibilistic representation of epistemic uncertainty can be combined with, and transformed into a probabilistic representation; in the present paper we show this with reference to a simple fault tree analysis. We apply an integrated (hybrid) probabilistic-possibilistic computational framework for the joint propagation of the epistemic uncertainty on the values of the (limiting relative frequency) probabilities of the basic events of the fault tree, and we use possibility-probability (probability-possibility) transformations for propagating the epistemic uncertainty within purely probabilistic and possibilistic settings. The results of the different approaches (hybrid, probabilistic, possibilistic) 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 critically examined. We conclude that the approaches relevant in a given setting depend on the purpose of the risk analysis, and that further research is required to make the possibilistic approaches operational in a risk analysis context.

Domains: Other

Enrico Zio, Terje Aven, Piero Baraldi, R. Flage. Probability and possibility based representations of uncertainty in fault tree analysis. Risk Analysis, 2013, 33 (1), pp.121-133. ⟨hal-00926381⟩