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Probability and Possibility‐Based Representations of Uncertainty in Fault Tree Analysis
Author(s) -
Flage Roger,
Baraldi Piero,
Zio Enrico,
Aven Terje
Publication year - 2013
Publication title -
risk analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.972
H-Index - 130
eISSN - 1539-6924
pISSN - 0272-4332
DOI - 10.1111/j.1539-6924.2012.01873.x
Subject(s) - probabilistic logic , fault tree analysis , uncertainty quantification , possibility theory , event tree , representation (politics) , computer science , context (archaeology) , event (particle physics) , uncertainty analysis , probabilistic risk assessment , probability theory , event tree analysis , propagation of uncertainty , mathematics , machine learning , artificial intelligence , algorithm , statistics , reliability engineering , engineering , law , fuzzy logic , biology , paleontology , quantum mechanics , fuzzy set , political science , physics , politics , simulation
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 this article, 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, and 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.