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Reliability and Safety Engineering pp 435–522Cite as

Uncertainty Management in Reliability/Safety Assessment

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Part of the book series: Springer Series in Reliability Engineering ((RELIABILITY,volume 0))

Abstract

A model (“the model of the world”) does the structuring of the problem for a physical situation at hand. This may occasionally be referred to as a “mathematical model.” There are two types of models of the world, deterministic and probabilistic. Newton’s laws are good examples of deterministic models. Many important phenomena cannot be modeled by deterministic expressions. For example, failure time of equipment exhibits variability that cannot be eliminated; given the present state of knowledge and technology, it is impossible to predict when the next failure will occur. This natural variability (or randomness) imposes the use of probabilistic models that include this uncertainty, which is central to reliability/risk analysis of engineering systems. This natural variability is sometimes referred to as “randomness” or “stochastic uncertainty,” commonly known as “aleatory uncertainty,” which cannot be reduced [1, 2].

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References

  1. NASA (2002) Probabilistic risk assessment procedures guide for NASA managers and practitioners. Version 1.1, NASA Report

    Google Scholar 

  2. Scott F, Lev RG (1996) Different methods are needed to propagate ignorance and variability. Reliability Engineering and System Safety 54:133–144

    Article  Google Scholar 

  3. IAEA (1992) Procedure for conducting probabilistic safety assessment of nuclear power plants (level 1). Safety series no. 50-P-4, International Atomic Energy Agency, Vienna

    Google Scholar 

  4. Abrahamsson M (2002) Uncertainty in quantitative risk analysis. Report 1024, Lund University

    Google Scholar 

  5. Morgan MG, Henrion M (1992) Uncertainty – A guide to dealing uncertainty in quantitative risk and policy analysis. Cambridge University Press, London

    Google Scholar 

  6. Rushdi AM, Kafrawy KF (1988) Uncertainty propagation in fault tree analyses using an exact method of moments. Microelectronics and Reliability 28:945–965

    Article  Google Scholar 

  7. Kafrawy KF, Rushdi AM (1990) Uncertainty analysis of fault tree with statistically correlated failure data. Microelectronics and Reliability 30:157–175

    Article  Google Scholar 

  8. Jackson PS, Hockenbury RW, Yeater ML (1981) Uncertainty analysis of system reliability and availability assessment. Nuclear Engineering and Design 68:5–29

    Article  Google Scholar 

  9. Zadeh LA (1965) Fuzzy sets. Information and Control 8:338–353

    Article  MATH  MathSciNet  Google Scholar 

  10. George JK, Yuan B (1995) Fuzzy sets and fuzzy logic. Prentice-Hall of India, New Delhi

    MATH  Google Scholar 

  11. Tanaka H, Fan LT, Lai FS, Toguchi K (1983) Fault tree analysis by fuzzy probability. IEEE Transactions on Reliability 32:453–457

    Article  MATH  Google Scholar 

  12. Modarres M (1985) Statistical uncertainty analysis in reactor risk estimation. Nuclear Engineering and Design 85:385–399

    Article  Google Scholar 

  13. Wu JS, Apostolakis GE, Okrent D (1990) Uncertainties in system analysis: probabilistic vs non probabilistic theories. Reliability Engineering and System Safety 30:163–181

    Article  Google Scholar 

  14. Helton JC (1993) Uncertainty and sensitivity analysis techniques for use in performance assessment for radioactive waste disposal. Reliability Engineering and System Safety 42:327–367

    Article  MathSciNet  Google Scholar 

  15. Soman KP, Misra KB (1993) Fuzzy fault tree analysis using resolution identity. Journal Fuzzy Mathematics 1:193–212

    MATH  MathSciNet  Google Scholar 

  16. Suresh PV, Babar AK, Venkatraj V (1996) Uncertainty in fault tree analysis: a fuzzy approach. Fuzzy Sets and Systems 83:135–141

    Article  Google Scholar 

  17. Karanki DR, Saraf RK, Kushwaha HS (2003) Uncertainty in reliability analysis of MCPS of TAPP 3 & 4, ICQRIT 2003, New Delhi

    Google Scholar 

  18. Ferson S, Hajago JG (2004) Arithmetic with uncertain numbers: rigorous and often best possible answers, Reliability Engineering and System Safety 85:135–152

    Article  Google Scholar 

  19. Regan HM, Ferson S, Berleant D (2004) Equivalence of methods for uncertainty propagation of real valued random variables. International Journal of Approximate Reasoning 36:1–30

    Article  MATH  MathSciNet  Google Scholar 

  20. Karanki DR et al (2004) A Study on uncertainty analysis of safety systems of advanced heavy water reactor using fuzzy set theory, PSAM7 – ESREL 2004, Berlin, Germany, pp 2283–2288

    Google Scholar 

  21. Antonio CFG, Nelson FFE (1999) FuzzyFTA: A fuzzy fault tree analysis for uncertainty analysis. Annals of Nuclear Energy 26:523–532

    Article  Google Scholar 

  22. Smith SA, Krishnamurthy T, Mason BH (2002) Optimized vertex method and hybrid reliability. American Institute of Aeronautics and Astronautics, 1465

    Google Scholar 

  23. Frantzich H (1988) Uncertainty and risk analysis in fire safety engineering. Doctoral dissertation, Department of Fire Safety Engineering, Lund University, Lund

    Google Scholar 

  24. Marquez AC, Heguedas AS, Iung B (2005) Monte Carlo-based assessment of system availability. Reliability Engineering and System Safety 88:273–289

    Article  Google Scholar 

  25. Bae HR, Grandhi RV, Canfield RA (2003) Uncertainty quantification of structural response using evidence theory. AIAA Journal 41(10):2062–2068

    Article  Google Scholar 

  26. Hofer E, Kloos M, Hausmann BK, Peschke J, Woltereck M (2002) An approximate epistemic uncertianty analysis approach in the presence of epistemic and aleatory uncertainties. Reliability Engineering and System Safety 77:229–238

    Article  Google Scholar 

  27. Bae H, Grandhi RV, Canfield RA (2004) Epistemic uncertainty quantification techniques including evidence theory for large scale structures. Computers and Structures 82:1101–1112

    Article  Google Scholar 

  28. Daniel B, Jianzhong Z (2004) Representation and problem solving with distribution envelope determination (DEnv). Reliability Engineering and System Safety 85(1–3):153–168

    Google Scholar 

  29. Winkler RL (1996) Uncertainty in probabilistic risk assessment. Reliability Engineering and System Safety 34:127–132

    Article  Google Scholar 

  30. Ahmed DR, Metcalf, Pegram JW (1981) Uncertainty propagation in probabilistic risk assessment: A comparative study. Nuclear Engineering and Design 68:1–3

    Article  Google Scholar 

  31. Keey RB, Smith CH (1985) The propagation of uncertainties in failure events. Reliability Engineering 10: 105–127

    Article  Google Scholar 

  32. Zhang Q (1990) A new approximate method for uncertainty propagation in system reliability analysis. Reliability Engineering and System Safety 29:261–275

    Article  Google Scholar 

  33. Mon DL, Cheng CH (1994) Fuzzy system reliability analysis for components with different membership functions. Fuzzy Sets and Systems 64:145–157

    Article  MathSciNet  Google Scholar 

  34. Helton JC (1994) Treatment of uncertainty in performance assessment for complex systems. Risk Analysis 483–511

    Google Scholar 

  35. Bae H, Grandhi RV, Canfield RA, (2004) An approximation approach for uncertainty quantification using evidence theory. Reliability Engineering and System Safety 86:215–225

    Article  Google Scholar 

  36. Misra KB, Weber GG (1989) A new method for fuzzy fault tree analysis. Microelectronics and Reliability 29(2):195–216

    Article  Google Scholar 

  37. Parry GW (1996) The characterization of uncertainty in probabilistic risk assessments of complex systems. Reliability Engineering and System Safety 54:119–126

    Article  Google Scholar 

  38. Cornell MEP (54) Uncertainties in risk analysis: Six levels of treatment. Reliability Engineering and System Safety 54:95–111

    Google Scholar 

  39. Tucker WT, Ferson S (2003) Probability bounds analysis in environmental risk assessments. Applied Biomathematics

    Google Scholar 

  40. Bruns M, Christiaan J, Paredis J (2006) Numerical methods for propagating imprecise uncertainty, Proceedings of IDETC 2006: ASME Design Engineering and Technical Conferences and Design Automation Conference, September 10–13, 2006, Philadelphia, PA, USA

    Google Scholar 

  41. Frey HC, Bharvirkar R (2002) Quantification of variability and uncertainty: A case study of power plant hazardous air pollutant emissions. In: Human and ecological risk analysis, D. Paustenbach, ed, John Wiley and Sons, New York, pp 587–617

    Google Scholar 

  42. Williamson RC, Downs T (1990) Probabilistic arithmetic I: numerical methods for calculating convolutions and dependency bounds. International Journal of Approximate Reasoning 4:89–158

    Article  MATH  MathSciNet  Google Scholar 

  43. Saltelli A, Marivoet J (1990) Non-parameter statistics in sensitivity analysis for model output: A comparison of selected techniques. Reliability Engineering and System Safety 28:229–253

    Article  Google Scholar 

  44. Borgonovo E (2006) Measuring uncertainty importance: Investigation and comparison of alternative approaches. Risk Analysis 26:1349–1361

    Article  Google Scholar 

  45. Iman RL, Conover WJ (1987) A measure of top down correlation. Technometrics 29(3):351–357

    Article  MATH  Google Scholar 

  46. Iman RL, Hora SC (1990) A robust measure of uncertainty importance for use in fault tree system analysis. Risk Analysis 10(3): 401–406

    Article  Google Scholar 

  47. Homma T, Saltelli A (1996) Importance measures in global analysis of nonlinear models. Reliability Engineering and System Safety 52:1–17

    Article  Google Scholar 

  48. Borgonovo E, Apostolakis GE, Tarantola S, Saltelli A (2003) Comparison of global sensitivity analysis techniques and importance measures in PSA. Reliability Engineering and System Safety 79:175–185

    Article  Google Scholar 

  49. Utkin LV (1993) Uncertainty importance of system components by fuzzy and interval probability. Microelectronics and Reliability 33(9):1357–1364

    Article  MathSciNet  Google Scholar 

  50. Utkin LV (1993) Uncertainty importance of multistate system components. Microelectronics and Reliability 33(13):2021–2029

    Article  Google Scholar 

  51. Karanki DR, Kushwaha HS, Verma AK, Srividya A (2009) A new uncertainty importance measure in fuzzy reliability analysis. International Journal of Performability Engineering 5(3):219–226

    Google Scholar 

  52. Cheng CH (1998) A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets and Systems 95:307–317

    Article  MATH  MathSciNet  Google Scholar 

  53. Ying W, Jian Y, Dong X, Kwai C (2006) On the centroids of fuzzy numbers. Fuzzy Sets and Systems 157:919–926

    Article  MATH  MathSciNet  Google Scholar 

  54. Zhi P, Ya Tai (1988) Variance importance of system components by Monte-Carlo. IEEE Transactions on Reliability 37(4): 421–423

    Article  Google Scholar 

  55. ISOGRAPH, FaultTree+10.1. Commercial software for fault tree analysis, UK

    Google Scholar 

  56. Hora SC (1996) Aleatory and epistemic uncertainty in probability elicitation with an example from hazardous waste management. Reliability Engineering and System Safety 54:217–223

    Article  Google Scholar 

  57. Apostolakis G (1999) The distinction between aleatory and epistemic uncertainties is important: An example from the inclusion of aging effects into PSA. Proceedings of PSA ’99, International topical meeting on probabilistic safety assessment, Washington, DC, pp 135–142

    Google Scholar 

  58. Ferson S et al (2004) Summary from the epistemic uncertainty workshop: Consensus amid diversity. Reliability Engineering and System Safety 85:355–369

    Article  Google Scholar 

  59. Stephen CH (1996) Aleatory and epistemic uncertainty in probability elicitation with an example from hazardous waste management. Reliability Engineering and System Safety 54:217–223

    Article  Google Scholar 

  60. Vose D (2000) Risk analysis – a quantitative guide. John Wiley & Sons, New York

    Google Scholar 

  61. Karanki DR, Kushwaha HS, Verma AK, Srividya A (2007) Quantification of epistemic and aleatory uncertainties in level-1 probabilistic safety assessment studies. Reliability Engineering and System Safety 92(7):947–956

    Article  Google Scholar 

  62. Jadhav PA (2007) Belief and plausibility analysis: Steady state heat conduction applications. DAE BRNS Theme meeting on methodology for quantification and propagation of uncertainty in safety assessment of NPP and fuel cycle facilities, pp 108–131

    Google Scholar 

  63. Kushwaha HS (2009) Uncertainty modeling and analysis. Bhabha Atomic Research Centre, Mumbai

    Google Scholar 

  64. Siu NO, Kelly DL (1998) Bayesian parameter estimation in probabilistic risk assessment. Reliability Engineering and System Safety 62:89–116

    Article  Google Scholar 

  65. USNRC (2003) Handbook of parameter estimation for probabilistic risk assessment. NUREG/CR-6823, US Nuclear Regulatory Commission, Washington, DC

    Google Scholar 

  66. Berger JO (1985) Statistical decision theory and Bayesian analysis, 2nd edn. Springer-Verlag, New York

    MATH  Google Scholar 

  67. Gelman A, Carlin JB, Stern HS, Rubin DB (1995) Bayesian data analysis. Chapman & Hall, London

    Google Scholar 

  68. USNRC (1975) Reactor safety study: an assessment of accidents in US commercial nuclear power plants, US Regulatory Commission, WASH-1400, Washington, DC

    Google Scholar 

  69. IEEE Standard-500 (1984) IEEE guide to the collection and presentation of electrical, electronic and sensing component reliability data for nuclear powered generation stations. Institute of Electrical and Electronic Engineers, Piscataway, NJ

    Google Scholar 

  70. USNRC (1990) Severe accident risk: an assessment for five US nuclear power plants. US Nuclear Regulatory Commission, NUREG-1150, Washington, DC

    Google Scholar 

  71. Swain AD, Guttman HE (1983) Handbook of human reliability analysis with emphasis on nuclear power applications. NUREG/CR-1278, US Nuclear Regulatory Commission, Washington, DC

    Google Scholar 

  72. Clemen RT, Winkler RL (1999) Combining probability distributions from experts in risk analysis. Risk Analysis 19(2):187–203

    Google Scholar 

  73. Ayyub BM (2001) Elicitation of expert opinions for uncertainty and risks. CRC Press, New York

    Book  Google Scholar 

  74. Karanki DR, Kushwaha HS, Verma AK, Srividya A (2008) Epistemic uncertainty propagation in reliability assessment of complex systems. International Journal of Performability Engineering 4(1):71–84

    Google Scholar 

  75. Tamatampalli S, Karanki DR (2003) Reliability analysis of main control power supply system of nuclear power plant. Internal report, Bhabha Atomic Research Centre, Mumbai

    Google Scholar 

  76. USNRC (1975) Reactor safety study. WASH-1400, NUREG-75/014, United States Nuclear Regulatory Commission

    Google Scholar 

  77. IAEA (1988) Component reliability data for use in probabilistic safety assessment. IAEA TECDOC 478, International Atomic Energy Agency, Vienna

    Google Scholar 

  78. Karanki DR, Kushwaha HS, Verma AK, Srividya A (2009) Uncertainty analysis based on probability bounds (p-box) approach in probabilistic safety assessment. Risk Analysis 29(5):662–675

    Article  Google Scholar 

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(2010). Uncertainty Management in Reliability/Safety Assessment. In: Reliability and Safety Engineering. Springer Series in Reliability Engineering, vol 0. Springer, London. https://doi.org/10.1007/978-1-84996-232-2_11

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  • DOI: https://doi.org/10.1007/978-1-84996-232-2_11

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84996-231-5

  • Online ISBN: 978-1-84996-232-2

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