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Probability and possibility-based representations of uncertainty in fault tree analysis
Roger Flage1, Piero Baraldi, Enrico Zio
1Department of Industrial Economics, Risk Management and Planning, Faculty of Science and Technology, University of Stavanger, 4036 Stavanger, Norway. roger.flage@uis.no.
Summary
This study explores using possibility theory to represent expert uncertainty in risk analysis when precise probabilities are difficult. It shows how this can be integrated with probabilistic methods for better uncertainty management.
Area of Science:
- Risk Analysis and Management
- Uncertainty Quantification
- Decision Science
Background:
- Expert knowledge is crucial for risk analysis but often imprecisely expressed.
- Traditional probabilistic methods may struggle with expert reluctance to assign exact probabilities.
- Epistemic uncertainty, stemming from incomplete knowledge, requires robust representation.
Purpose of the Study:
- To investigate the application of possibility theory for representing and propagating expert epistemic uncertainty in risk analysis.
- To demonstrate the integration of possibilistic and probabilistic frameworks for uncertainty analysis.
- To compare different approaches for quantifying uncertainty in fault tree analysis.
Main Methods:
- Utilized the theory of possibility to handle imprecise probability assignments from experts.
- Developed and applied an integrated probabilistic-possibilistic computational framework.
- Employed possibility-probability and probability-possibility transformations for uncertainty propagation.
- Analyzed a simple fault tree to illustrate the methods.
Main Results:
- The study successfully demonstrated the combination of possibilistic and probabilistic representations of epistemic uncertainty.
- Comparison of hybrid, purely probabilistic, and purely possibilistic approaches revealed differences in uncertainty representation for the top event probability.
- The integrated framework allows for joint propagation of uncertainty on basic event probabilities.
Conclusions:
- The choice of risk analysis approach (probabilistic, possibilistic, or hybrid) depends on the specific analysis goals.
- Possibilistic methods offer a valuable alternative for representing expert uncertainty when precise probabilities are unavailable.
- Further research is needed to operationalize possibilistic approaches within practical risk analysis contexts.
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