Interpretations of alternative uncertainty representations in a reliability and risk analysis context

Reliability Engineering and System Safety

Volumn 96, Issue 3, 2011, Pages 353-360

  Aven, T ^a  

^a UNIVERSITY OF STAVANGER   (Norway)

Author keywords

Evidence theory; Fuzzy probability; Imprecise (interval) probability; Interpretation; Possibility theory; Risk and reliability analysis; Subjective probabilities; Uncertainties

Indexed keywords

EVIDENCE THEORIES; FUZZY PROBABILITY; IMPRECISE (INTERVAL) PROBABILITY; INTERPRETATION; POSSIBILITY THEORY; SUBJECTIVE PROBABILITY; UNCERTAINTIES;

RELIABILITY ANALYSIS; RELIABILITY THEORY; RISK ANALYSIS; RISK ASSESSMENT; UNCERTAINTY ANALYSIS;

QUALITY ASSURANCE;

EID: 78650840086     PISSN: 09518320     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ress.2010.11.004     Document Type: Article

References (55)

1. E. de Rocquigny, N. Devictor, S. Tarantola, A guide to quantitative uncertainty management 2008 Wiley Chichester
2. J.C. Helton, J.D. Johnson, and W.L. Oberkampf An exploration of alternative approaches to the representation of uncertainty in model predictions Reliability Engineering and System Safety 85 2004 39 71
3. T. Bedford, and R.M. Cooke Probabilistic risk analysis: foundations and methods 2001 Cambridge University Press Cambridge
4. R.J. Breeding, J.C. Helton, E.D. Gorham, and F.T. Harper Summary description of the methods used in the probabilistic risk assessments for NUREG-1150 Nuclear Engineering and Design 135 1 1992 1 27
5. J.C. Helton, and R.J. Breeding Calculation of reactor accident safety goals Reliability Engineering and System Safety 39 2 1993 129 158
6. J.C. Helton, and C.J. Sallaberry Treatment of Uncertainty in Performance Assessments for the Geological Disposal of Radioactive Waste J. Ahn, M.J. Apted, Geological reopositories for safe disposal of spent fuels and radioactive materials: advanced technologies 2010 Woodhead Publishing Cambridge, UK 547 579
7. M. Modarres What every engineer should know about reliability and risk analysis 1993 Marcel Dekker, Inc. N.Y.
8. E. Zio An introduction to the basics of reliability and risk analysis 2006 World Scientific London
9. T. Aven Foundations of risk nalysis: a knowledge and decision-oriented perspective 2003 Wiley Chichester
10. N.D. Singpurwalla Reliability and risk: A Bayesian perspective 2006 Wiley Chichester
11. G.W. Parry, and P.W. Winter Characterization and evaluation of uncertainty in probabilistic risk analysis Nuclear Safety 22 1 1981 28 42
12. G.W. Parry The characterization of uncertainty in probabilistic risk assessments of complex systems Reliability Engineering and System Safety 54 23 1996 119 126
13. F.O. Hoffman, and J.S. Hammonds Propagation of uncertainty in risk assessments: the need to distinguish between uncertainty due to lack of knowledge and uncertainty due to variability Risk Analysis 14 5 1994 707 712
14. J.C. Helton Treatment of uncertainty in performance assessments for complex systems Risk Analysis 14 4 1994 483 511
15. J.C. Helton, and D.E. Burmaster Guest editorial: treatment of aleatory and epistemic uncertainty in performance assessments for complex systems Reliability Engineering and System Safety 54 23 1996 91 94
16. J.C. Helton Uncertainty and Sensitivity Analysis in the Presence of Stochastic and Subjective Uncertainty Journal of Statistical Computation and Simulation 57 14 1997 3 76
17. M.E. Pat-Cornell Uncertainties in risk analysis: six levels of treatment Reliability Engineering and System Safety 54 23 1996 95 111
18. D.V. Lindley Understanding uncertainty 2006 Wiley Hoboken, NJ
19. F.J. Anscombe, and R.J.A. Aumann Definition of subjective probability The Annals of Mathematical Statistics 34 1 1963 199 205
20. J.M. Bernardo, and A.F.M. Smith Bayesian theory 1994 Wiley Chichester
21. Stanford encyclopedia of philosophy Interpretations of probability. December 31.〈 http://plato.stanford.edu/entries/probability-interpret/ 〉; 2009 [accessed 01.11.10].
22. T. Aven Some reflections on uncertainty analysis and management Reliability Engineering and System Safety 95 2010 195 201
23. T. Aven On the need for restricting the probabilistic analysis in risk assessments to variability Risk Analysis 30 3 2010 354 360 With discussion pp. 381384
24. D. Dubois Possibility theory and statistical reasoning Computational Statistics & Data Analysis 51 2006 47 69
25. M.B. Anoop, and K.B. Rao Determination of bounds on failure probability in the presence of hybrid uncertainties Sadhana 33 2008 753 765
26. R.L. Winkler Uncertainty in probabilistic risk assessment Reliability Engineering and System Safety 85 1996 127 132
27. W. North Probability theory and consistent reasoning Risk Analysis 30 2010 377 380
28. R. Cooke The Anatomy of the squizzel. The role of operational definitions in representing uncertainty Reliability Engineering and System Safety 85 2004 313 319
29. C. Baudrit, and D. Dubois Practical representations of incomplete probabilistic knowledge Computational Statistics & Data Analysis 51 2006 86 108
30. D. Dubois Representation, propagation and decision issues in risk analysis under incomplete probabilistic information Risk Analysis 30 2010 361 368
31. T. Aven, and E. Zio Some considerations on the treatment of uncertainties in risk assessment for practical decision-making Reliability Engineering and System Safety 2011 96
32. T. Aven, and S. Guikema Whose uncertainty assessments (probability distributions) does a risk assessment report: the analysts or the experts? Reliability Engineering and System Safety 2010 Revised and resubmitted to
33. G. Boole An investigation of the laws of thought on which are founded the mathematical theories of logic and probabilities 1854 Walton and Maberly London
34. B. de Finetti Theory of probability 1974 Wiley New York
35. V.P. Kuznetsov Interval statistical models 1991 Radio i Svyaz Moscow [in Russian]
36. P. Walley Statistical reasoning with imprecise probabilities 1991 Chapman and Hall N.Y.
37. Flage R, Aven T, Zio E Alternative representations of uncertainty in reliability and risk analysisreview and discussion. In: Martorell S, Guedes Soares C, Barnett J, editors. Safety, reliability and risk analysis. Theory, methods and applications. Proceedings of the European safety and reliability conference 2009. (ESREL 2009), Valencia, Spain, 2225 September 2008, London: CRC Press; 2009. p. 208191.
38. S. Ferson, and L.R. Ginzburg Different methods are needed to propagate ignorance and variability Reliability Engineering and System Safety 54 1996 133 144
39. Coolen FPA, Utkin LV Imprecise probability: a concise overview. In: Aven T, Vinnem JE, editors. Risk, reliability and societal safety: Proceedings of the European safety and reliability conference (ESREL), Stavanger, Norway, London: Taylor & Francis; 2527 June 2007. p. 195965.
40. I. Kozine, and L. Utkin Processing unreliable judgements with an imprecise hierarchical model Risk Decision and Policy 7 2002 1 15
41. D. Dubois, and H. Prade Fuzzy sets, probability and measurement European Journal of Operations Research 40 1989 135 154
42. P. Baraldi, and E. Zio A combined Monte Carlo and possibilistic approach to uncertainty propagation in event tree analysis Risk Analysis 28 2008 1309 1325
43. J.C. Helton, J.D. Johnson, and W.L. Oberkampf An Exploration of alternative approaches to the representation of uncertainty in model predictions Reliability Engineering and System Safety 85 13 2004 39 71
44. J.C. Helton, J.D. Johnson, W.L. Oberkampf, and C.J. Sallaberry Representation of analysis results involving aleatory and epistemic uncertainty International Journal of General Systems 39 6 2010 605 646
45. A.P. Dempster Upper and lower probabilities induced by a multivalued mapping Annals of Mathematical Statistics 38 1967 325 339
46. G.A. Shafer Mathematical theory of evidence 1976 Princeton University Press Princeton
47. G. Shafer Perspectives on the theory and practice of belief functions International Journal of Approximate Reasoning 4 1990 323 362
48. P. Smets What is Dempster-Shafers model? R.R. Yager, M. Fedrizzi, J. Kacprzyk, Advances in the DempsterShafer theory of evidence 1994 Wiley 5 34
49. Dubois D. Uncertainty theories: a unified view. In: IEEE conference on cybernetic systems. Dublin (Ireland), 09/2007.
50. L.A. Zadeh Probability measures of fuzzy events Journal of Mathematical Analysis and Applications 23 1968 421 427
51. L.A. Zadeh Fuzzy sets Information and Control 8 1965 338 353
52. Bilgic T, Turksen IB. Elicitation of membership functions: how far can theory take us? In: Proceedings of the Fuzzy-IEEE 97 http://www.ie.boun.edu.tr/ ∼taner/publications/papers/fuzzieee97.pdf;1997 [accessed 02.11.10].
53. L.A. Zadeh Discussion: probability theory and fuzzy logic are complementary rather than competitive Technometrics 37 3 1995 271 276
54. N.D. Singpurwalla, and J.M. Booker Membership functions and probability measures of fuzzy sets Journal of the American Statistical Association 99 2004 867 889 [with discussion]
55. D.V. Lindley The philosophy of statistics The Statistician 49 3 2000 293 337