Uncertainty analysis in fault tree models with dependent basic events

Risk Analysis

Volumn 33, Issue 6, 2013, Pages 1146-1173

  Pedroni, Nicola ^a   Zio, Enrico ^a,b  

^a POLITECNICO DI MILANO   (Italy)

^b ECOLE CENTRALE PARIS   (France)

Author keywords

Epistemically uncertain probabilities; Fault tree; Objective and epistemic dependences

Indexed keywords

EPISTEMIC DEPENDENCES; FAULT TREE MODEL; FAULT-TREES; UNCERTAIN PROBABILITIES;

PHYSIOLOGY; RISK ANALYSIS; SAFETY ENGINEERING;

UNCERTAINTY ANALYSIS;

PROBABILITY; RISK ASSESSMENT; RISK PERCEPTION; UNCERTAINTY ANALYSIS;

EID: 84879096100     PISSN: 02724332     EISSN: 15396924     Source Type: Journal    
DOI: 10.1111/j.1539-6924.2012.01903.x     Document Type: Article

References (88)

1. Henley EJ, Kumamoto H. Probabilistic Risk Assessment. New York: IEEE Press, 1992.
2. USNRC. Guidance on the Treatment of Uncertainties Associated with PRAs in Risk-Informed Decision Making. NUREG-1855, Washington, DC: US Nuclear Regulatory Commission, 2009.
3. NASA. Risk-Informed Decision Making Handbook. NASA/SP-2010-576-Version 1.0. Washington, DC: Office of Safety and Mission Assurance, NASA Headquarters, 2010.
4. Epstein S, Rauzy A. Can we trust PRA? Reliability Engineering & System Safety, 2005; 88(3):195-205.
5. Cepin M. Analysis of truncation limit in probabilistic safety assessment. Reliability Engineering & System Safety, 2005; 87(3):395-403.
6. Lindley DV, Singpurwalla ND. Reliability (and fault tree) analysis using expert opinions. Journal of the American Statistical Association, 1986; 81(393):87-90.
7. Apostolakis GE. The concept of probability in safety assessment of technological systems. Science, 1990; 250(4986):1359-1364.
8. Aven T. Foundations of Risk Analysis: A Knowledge and Decision-Oriented Perspective. Chichester: Wiley, 2003.
9. Helton JC, Oberkampf W. Alternative representations of epistemic uncertainties. Reliability Engineering and System Safety, 2004; 85(1-3):1-10.
10. Limbourg P, de Rocquigny E. Uncertainty analysis using evidence theory - Confronting level-1 and level-2 approaches with data availability and computational constraints, Reliability Engineering and System Safety, 2010; 95(5):550-564.
11. Apostolakis GE, Kaplan S. Pitfalls in risk calculations. Reliability Engineering, 1981; 2(2):135-145.
12. Huang D, Chen T, Wang MJ. A fuzzy set approach for event tree analysis. Fuzzy Sets and Systems, 2001; 118:153-165.
13. NUREG-CR-6850. EPRI/NRC-RES Fire PRA Methodology for Nuclear Power Facilities, Volume 2: Detailed Methodology. US Nuclear Regulatory Commission, 2005.
14. USNRC. An Approach for Using Probabilistic Risk Assessment in Risk-Informed Decisions on Plant-Specific Changes to the Licensing Basis. NUREG-1.174 - Revision 1, Washington, DC: US Nuclear Regulatory Commission, 2002.
15. Aven T. On the need for restricting the probabilistic analysis in risk assessments to variability. Risk Analysis, 2010; 30(3):354-360.
16. Aven T. Interpretations of alternative uncertainty representations in a reliability and risk analysis context. Reliability Engineering & System Safety, 2011; 96(3):353-360.
17. Aven T, Steen R. The concept of ignorance in a risk assessment and risk management context. Reliability Engineering and System Safety, 2010; 95(11):1117-1122.
18. Aven T, Zio E. Some considerations on the treatment of uncertainties in risk assessment for practical decision making. Reliability Engineering and System Safety, 2010; 96(1):64-74.
19. Ferson S, Ginzburg L, Akcakaya R. Whereof one cannot speak: When input distributions are unknown. Applied Biomathematics Report, Setauket, NY: Applied Biomathematics Inc., 1998. Available at http://www.ramas.com/whereof.pdf.
20. Klir GJ, Yuan B. Fuzzy Sets and Fuzzy Logic: Theory and Applications. Upper Saddle River, NJ: Prentice-Hall, 1995.
21. Tanaka H, Fan LT, Lai FS. Fault tree analysis by fuzzy probability. IEEE Transactions on Reliability, 1983; 32:453-457.
22. Liang GS, Wang MJJ. Fuzzy fault tree analysis using failure possibility. Microelectronics Reliability, 1993; 33(4):583-597.
23. Huang HZ, Tong X, Zuo M. Posbist fault tree analysis of coherent systems. Reliability Engineering and System Safety, 2004; 84(2):141-148.
24. Yuhua D, Datao Y. Estimation of failure probability of oil and gas transmission pipelines by fuzzy fault tree analysis. Journal of Loss Prevention in the Process Industries, 2005; 18:83-88.
25. Ferdous R, Khan F, Veitch B, Amyotte PR. Methodology for computer aided fuzzy fault tree analysis. Process Safety and Environmental Protection, 2009; 87:217-226.
26. Misra KB, Weber GG. A new method for fuzzy fault tree analysis. Microelectronics Reliability, 1989; 29(2):195-216.
27. Soman KP, Misra KB. Fuzzy fault tree analysis using resolution identity and extension principle. International Journal of Fuzzy Mathematics, 1993; 1:193-212.
28. Suresh PV, Babar AK, Venkat Raj V. Uncertainty in fault tree analysis: A fuzzy approach. Fuzzy Sets and Systems, 1996; 83:135-141.
29. Baudrit C, Dubois D. Practical representations of incomplete probabilistic knowledge. Computational Statistics & Data Analysis, 2006; 51(1):86-108.
30. Baudrit C, Dubois D, Guyonnet D. Joint propagation and exploitation of probabilistic and possibilistic information in risk assessment. IEEE Transactions on Fuzzy Systems, 2006; 14(5):593-608.
31. Baudrit C, Dubois D, Perrot N. Representing parametric probabilistic models tainted with imprecision. Fuzzy Sets and System, 2008; 159(15):1913-1928.
32. Dubois D. Possibility theory and statistical reasoning. Computational Statistics & Data Analysis, 2006; 51:47-69.
33. Dubois D, Prade H. Possibility Theory: An Approach to Computerized Processing of Uncertainty. New York: Plenum Press, 1988.
34. Baraldi P, Zio E. A combined Monte Carlo and possibilistic approach to uncertainty propagation in event tree analysis. Risk Analysis, 2008; 28(5):1309-1326.
35. Flage R, Baraldi P, Ameruso F, Zio E, Aven T. Handling epistemic uncertainties in fault tree analysis by probabilistic and possibilistic approaches. Pp. 1761-1768 in Bris R, Guedes Soares C, Martorell S (eds). Reliability, Risk and Safety: Theory and Applications. Supplement Proceedings of the European Safety and Reliability Conference 2009 (ESREL 2009), Prague, Czech Republic, 7-10 September 2009. Boca Raton: Taylor & Francis, 2010.
36. Flage R, Baraldi P, Zio E, Aven T. Possibility-probability transformation in comparing different approaches to the treatment of epistemic uncertainties in a fault tree analysis. Pp. 714-721 in Ale B, Papazoglu IA, Zio E (eds). Reliability, Risk and Safety - Proceedings of the European Safety and Reliability (ESREL) 2010 Conference, Rhodes, Greece, 5-9 September 2010. London, UK: Taylor & Francis Group, 2010.
37. Limbourg P, Savic R, Petersen J, Kochs HD. Fault tree analysis in an early design stage using the Dempster-Shafer theory of evidence. Pp. 713-722 in Aven T, Vinnem JE (eds). Risk, Reliability and Societal Safety-Proceedings of the European Safety and Reliability (ESREL) 2007 Conference, Stavanger, Norway. London, UK: Taylor & Francis Group, 2007.
38. Limbourg P, Savić R, Petersen J, Kochs H-D. Modelling uncertainty in fault tree analyses using evidence theory. Journal of Risk and Reliability, 2008; 222(3):291-301.
39. Ferson S, Kreinovich V, Ginzburg L, Sentz K, Myers DS. Constructing probability boxes and Dempster-Shafer structures. Sandia National Laboratories, Technical Report SAND2002-4015, Albuquerque, NM, 2003.
40. Ferson S, Nelsen RB, Hajagos J, Berleant DJ, Zhang J, Tucker WT, Ginzburg LR, Oberkampf WL. Dependence in probabilistic modeling, Dempster-Shafer theory, and probability bounds analysis. Technical Report SAND2004-3072, Albuquerque, NM, 2004.
41. Helton JC, Johnson JD, Oberkampf WL, Storlie CB. A sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory. Computer Methods in Applied Mechanics and Engineering, 2007; 196:3980-3998.
42. Helton JC, Johnson JD, Oberkampf WL, Sallaberry CJ. Representation of analysis results involving aleatory and epistemic uncertainty. Sandia National Laboratories, Technical Report SAND2008-4379, Albuquerque, NM, 2008.
43. Sentz K, Ferson S. Combination of evidence in Dempster-Shafer theory. Sandia National Laboratories, Technical Report SAND 2002-0835, Albuquerque, NM, 2002.
44. Shafer G. A Mathematical Theory of Evidence. Princeton, NJ: Princeton University Press, 1976.
45. Ferson S, Hajagos JG. Arithmetic with uncertain numbers: Rigorous and (often) best possible answers. Reliability Engineering and System Safety, 2004; 85:135-152.
46. Ferson S, Tucker WT. Sensitivity in risk analyses with uncertain numbers. Technical Report SAND2006-2801, Setauket, NY, 11733, 2006.
47. Ferson S, Kreinovich V, Hajagos J, Oberkampf W, Ginzburg L. Experimental uncertainty estimation and statistics for data having interval uncertainty. Technical Report SAND2007-0939, Setauket, NY, 11733, 2007.
48. Ferson S, Van den Brink P, Estes TL, Gallagher K, O'Connor R, Verdonck F. Bounding uncertainty analyses. In Warren-Hicks WJ, Hart A. Application of Uncertainty Analysis to Ecological Risks of Pesticides. Pensacola and Boca Raton, FL: SETAC and CRC Press, 2010.
49. Moore RE. Methods and Applications of Interval Analysis. Philapdelphia, PA: SIAM, 1979.
50. USNRC. Procedure for Analysis of Common-Cause Failures in Probabilistic Safety Analysis. Technical report NUREG/CR-5801 (SAND91-7087), Washington, DC: Division of Safety Issue Resolution, Office of Nuclear Regulatory Research, U.S. Nuclear Regulatory Commission, 1993.
51. USNRC. Common-Cause Failure Database and Analysis System: Event Data Collection, Classification, and Coding. Technical report NUREG/CR-6268, Washington, DC: U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research, 2007.
52. Zio E. Computational Methods for Reliability and Risk Analysis. Singapore: World Scientific Publishing, 2009.
53. Watts DJ. A simple model of global cascades on random networks. Proceedings of the National Academy of Science USA, 2002; 99(9):5766-5771.
54. Guimerà R, Arenas A, Dìaz-Guilera A, Giralt F. Dynamical properties of model communication networks. Physical Review E, 2002; 66: 026704.
55. Sansavini G, Hajj MR, Puri IK, Zio E. A deterministic representation of cascade spreading in complex networks. EPL, 2009; 87(4):1-4, art. no. 48004.
56. Zio E, Sansavini G. Modeling interdependent network systems for identifying cascade-safe operating margins. IEEE Transactions on Reliability, 2011; 60(1):94-101.
57. Zio E, Sansavini G. Component criticality in failure cascade processes of network systems. Risk Analysis, 2011; 31(8):1196-1210.
58. Fréchet M. Généralisations du théorème des probabilités totales. Fundamenta Mathematica, 1935; 25:379-387.
59. Frank MJ, Nelsen RB, Schweizer B. Best-possible bounds for the distribution of a sum-a problem of Kolmogorov. Probability Theory and Related Fields, 1987; 74:199-211.
60. Sadiq R, Saint-Martin E, Kleiner Y. Predicting risk of water quality failures in distribution networks under uncertainties using fault-tree analysis. Urban Water, 2008; 5(4):287-304.
61. Berleant D, Goodman-Strauss C. Bounding the results of arithmetic operations on random variables of unknown dependency using intervals. Reliable Computing, 1998; 4:147-165.
62. Berleant D, Zhang J. Representation and problem solving with distribution envelope determination (DEnv). Reliability Engineering and System Safety, 2004; 85:153-168.
63. Berleant D, Zhang J. Using Pearson correlation to improve envelopes around the distributions of functions. Reliable Computing, 2004; 10:139-161.
64. Berleant D, Xie L, Zhang J. Statool: A tool for distribution envelope determination (DEnv), an interval-based algorithm for arithmetic on random variables. Reliable Computing, 2003; 9(2):91-108.
65. Berleant D, Anderson G, Goodman-Strauss C. Arithmetic on bounded families of distributions: A DEnv algorithm tutorial. Pp. 183-210 in Hu C, Kearfott RB, de Korvin A and Kreinovich V (eds). Knowledge Processing with Interval and Soft Computing. London, UK: Springer-Verlag, 2008.
66. Vaurio JK. Treatment of general dependencies in system fault-tree and risk analysis. IEEE Transactions on Reliability, 2002; 51(3):278-287.
67. Vaurio JK. Consistent mapping of common cause failure rates and alpha factors. Reliability Engineering and System Safety, 2007; 92(5):628-645.
68. Karanki DR, Dang VN. Quantification of uncertainty in fault tree analysis with correlated basic events. Pp. 1619-1628 in Ale B, Papazoglu IA, Zio E (eds). Reliability, Risk and Safety - Proceedings of the European Safety and Reliability (ESREL) 2010 Conference, Rhodes, Greece, 5-9 September 2010. London, UK: Taylor & Francis Group, 2010.
69. Li H. Hierarchical Risk Assessment of Water Supply Systems. Ph.D. thesis, Loughborough University, Leicestershire, UK, 2007.
70. Ferdous R, Khan F, Sadiq R, Amyotte P, Veitch B. Fault and event tree analyses for process systems risk analysis: Uncertainty handling formulations. Risk Analysis, 2011; 31(1):86-107.
71. Zhang Q. A general method dealing with correlations in uncertainty propagation in fault trees. Reliability Engineering and System Safety, 1989; 26(3):231-247.
72. Zhang Q. A method dealing with correlations in uncertainty propagation by using traditional correlation coefficients. Reliability Engineering and System Safety, 1993; 41(2):107-114.
73. Rushdi AM, Kafrawy KF. Uncertainty propagation in fault tree analyses using an exact method of moments. Microelectronics and Reliability, 1988; 28:945-965.
74. Kafrawy KF, Rushdi AM. Uncertainty analysis of fault tree with statistically correlated failure data. Microelectronics and Reliability, 1990; 30:157-175.
75. Karanki DR, Jadhav PA, Chandrakar A, Srividya A, Verma AK. Uncertainty analysis in PSA with correlated input parameters. International Journal of Systems Assurane Engineering Management, 2010; 1:66-71.
76. Huang B, Du X. A robust design method using variable transformation and Gauss-Hermite integration. International Journal for Numerical Methods in Engineering, 2006; 66:1841-1858.
77. Kalos MH, Whitlock PA. Monte Carlo Methods. Volume I: Basics. New York: Wiley, 1986.
78. Marseguerra M, Zio E. Basics of the Monte Carlo Method with Application to System Reliability. Hagen, Germany: LiLoLe-Verlag GmbH, 2002.
79. Karanki DR, Kushwaha HS, Verma AK, Ajit S. Uncertainty analysis based on probability bounds (P-Box) approach in probabilistic safety assessment. Risk Analysis, 2009; 29(5):662-675.
80. Regan HM, Ferson S, Berleant D. Equivalence of five methods for bounding uncertainty. International Journal of Approximate Reasoning, 2004; 36:1-30.
81. Tonon F. Using random set theory to propagate epistemic uncertainty through a mechanical system. Reliability Engineering and System Safety, 2004; 85:169-181.
82. Couso I, Moral S. Independence concepts in evidence theory. International Journal of Approximate Reasoning, 2010; 51:748-758.
83. Couso I, Moral S, Walley P. Examples of independence for imprecise probabilities. Pp. 121-130 in de Cooman G, Cozman FF, Moral S, Walley P (eds). Proceedings of the First International Symposium on Imprecise Probability and Their Applications. Imprecise Probabilities Project, Universiteit Gent, Belgium, 1999.
84. Couso I, Moral S, Walley P. A survey of concepts of independence for imprecise probabilities. Risk Decision and Policy, 2000; 5:165-181.
85. Dubois D, Prade H, Sandri S. On possibility/probability transformations. Pp. 103-112 in Lowen R, Roubens M (eds). Fuzzy Logic: State of the Art. Dordrecht, The Netherlands: Kluwer Academic Publishers, 1993.
86. Smets P. Constructing the pignistic probability function in a context of uncertainty. Pp. 29-39 in Henrion M, Shachter RD, Kanal LN, Lemmer JF (eds). Uncertainty in Artificial Intelligence 5. Amsterdam, The Netherlands: North-Holland Publishing Co., 1990.
87. Dubois D, Foulloy L, Mauris G, Prade H. Probability-possibility transformations, triangular fuzzy sets, and probabilistic inequalities. Reliable Computing, 2004; 10:273-297.
88. Dubois D, Prade H, Smets P. A definition of subjective possibility. International Journal of Approximate Reasoning, 2008; 48:352-364.