The estimation of failure rates for low probability events

Progress in Nuclear Energy

Volumn 31, Issue 4, 1997, Pages 373-476

  Williams, M M R ^a   Thorne, M C ^a  

^a Electrowatt House   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038905782     PISSN: 01491970     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0149-1970(96)00022-4     Document Type: Article

References (76)

1. Abramowitz, M. and Stegun, I.A. (1970) "Handbook of Mathematical Functions", Dover Publication.
2. Apostolakis, G. and Mosleh, A. (1979) "Expert opinion and statistical evidence: an application to reactor core melt frequency", Nucl Sci. andEng. 70, 135.
3. Apostolakis, G. (1981) "Bayesian methods in risk assessment", Advances in Nuclear Science and Technology, 13, Eds. J.D. Lewins and M. Becker, John Wiley and Sons.
4. Benford, F (1938) "The Law of Anomalous Numbers". Proc. Am. Philos. Soc., 78(4):551-572 .
5. Bertrand, J L F (1907) "Cale des Probabilits, Gauthier-Villars, Paris.
6. Bonano, E.J, and Apostolakis, G. (1990) "Theoretical foundations and practical issues for using expert judgements in uncertainty analysis of high-level radioactive waste disposal", Sandia National Laboratories Report SAND90-2672J
7. Box, G.E.P. and Tiao, G.C. (1973). "Bayesian Inference in Statistical Analysis", Addison-Wesley Publishing Company.
8. Carnap, R (1952) "The Continuum of Inductive Methods". Chicago: University of Chicago Press.
9. Chernoff, H and Moses, L.E. (1959) "Elementary Decision Theory", New York: Wiley.
10. Critchley, O.H. (1986) "A new treatment of low probability events with particular application to nuclear power plants", Prog. Nucl. Energy 3, 301.
11. de Finetti, B (1965) "Methods for Discriminating Levels of Partial Knowledge Concerning a Test Items". Br. J. Math. Stat. Psychol., 18: 87-123.
12. de Finetti, B (1974) "Theory of Probability", Vols 1 and 2, John Wiley and Sons
13. Dutta, M (1966) "On maximum entropy estimation," Sankhya, ser. A, Vol 28, pt 4, pp. 319-328.
14. Feduccia, A,J and J. Klion,"How accurate are reliability predictions?" Proc. Annual Symposium on Reliability, Mass, USA (1968).
15. Feibstein, A (1958) "Foundations of Information Theory". New York L McGraw-Hill.
16. Fraser, D A S (1966) "On fiducial inference," Ann. Math. Statist., vol. 32, pp. 661-676.
17. Gibbs, J W , "Elementary Principles in Statistical Mechanics". New Haven, Conn: Yale University Press, 1902.
18. Good, I.J. (1950) "Probability and weighing of evidence", Griffin, London
19. Good, I.J. (1959) "Kinds of probability", Science 129, 443.
20. Good, I.J. (1965) "The estimation of probabilities", MIT Press.
21. Good, I J (1963) "Maximum entropy for hypothesis formulation," Ann. Math. Statist. Vol 34, pp. 911-930.
22. Green, A.E. & Bourne, A.J. (1972) "Reliability Technology", John Wiley.
23. Haldane, J.B.S. (1948) "The precision of observed values of small frequencies" Biometrika 35, 297.
24. Harr, A (1933) "Der Massbegriff in der Theories der kontinuierlichen Gruppen," Ann. Math., 34, pp. 147-169.
25. Hartigan, J (1964) "Invariant prior distributions," Ann. Math. Statist., 35, pp. 836-845.
26. Huzurbazar, V S (1955) "Exact Forms of Some Invariants for Distributions Admitting Sufficient Statistics", Biometrika, 42: 533-537.
27. International Standard CEI-IEC 605-4 (1986). "Equipment reliability testing, part 4: procedures for determining point estimates and confidence limits for equipment reliability determination tests."
28. Jaynes, E.T (1963) "New engineering applications of information theory," in Proc. 1st Symp. on Engineering Applications of Random Function Theory and Probability, J L Bogdanoff and F Kozin, Eds. New York: Wiley, pp. 163-203.
29. Jaynes, E.T. (1968) "Prior probabilities", IEEE Trans of Systems Science & Cybernetics SSC-4, 227.
30. Jaynes, E.T.(1963) "Information theory and statistical mechanics," in Statistical Physics, Vol 3, K W Ford, Ed. New York: W A Benhamin, Inc., ch 4, pp. 182-218.
31. Jaynes, E T , (1967)"Foundations of probability theory and statistical mechanics," in Delaware Seminar in the Foundations of Physics, M Bunge, Ed. Berlin: Springer, ch. 6.
32. Jaynes, E T ,(1957) "Information theory and statistical mechanics", pt I, Phys. Rev. Vol 106, pp. 620-630, March 1957; pt II, ibid, Vol 108, pp. 171-191, October 1957.
33. Jaynes, E T ,(1957) "Information theory and statistical mechanics", pt I, Phys. Rev. Vol 106, pp. 620-630, March 1957; pt II, ibid, Vol 108, pp. 171-191, October 1957.
34. Jeffreys, H (1948) "Theory of Probability", Oxford University Press.
35. Jeffreys, H (1957) "Scientific inference", Cambridge University Press.
36. Kaplan, S and Garrick, B.J. (1979) "On the use of Bayesian reasoning in safety and reliability decisions - three examples", Nuclear Technology 44, 231.
37. Kaplan, S (1983) "On a two-stage Bayesian procedure for determining failure rates from experimental data",IEEE Trans. Power Apparatus and Systems, Vol PAS-102, 195.
38. Kaplan, S et al. (1989) "A methodology for assessing the reliability of 'boxes'", Reliability Engineering and System Safety, 26, 249.
39. Kahneman, D and A Tversky,(1972) "Intuitive Prediction." Oreg. Res. Inst. Bull., 12(4).
40. Kendall, M G and A Stuart, (1961) "The Advanced Theory of Statistics", Vol 2. New York: Hafner.
41. Kokoska, S. and Nevison, C (1989) "Statistical Tables and Formulae" Springer-Verlag.
42. Kullback, S (1959) "Information Theory and Statistics". New York: Wiley.
43. Kyburg, H.R. & Smokler, H.E. (1964) "Studies in subjective probabilities", John Wiley.
44. Lehmann, E L (1959)"Testing Statistical Hypotheses". New York: Wiley.
45. Maisel, L. (1971) "Probability, Statistics and Random Processes" Simon & Schuster Technical Outline Series.
46. McCormick, N.J. (1981) "Reliability and Risk Analysis: methods and nuclear power applications", Academic Press Inc.
47. Mosleh, A. ,Bier, V.M. and Apostolakis, G (1987) "Methods for the elicitation and use of expert opinion in risk assessment", NUREG/CR-4962
48. Mosleh, A. ,Bier, V.M. and Apostolakis, G (1988) "A critique of current practice for the use of expert opinion in probabilistic risk assessment", Reliability Engineering and System Safety 20, 63.
49. Parry, G.W. and Winter, P.W. (1981)"Characterisation and evaluation of uncertainty in probabilistic risk analysis", Nuclear Safety 22 , 28.
50. Poincare, H (1912) "Calcul des Probabilities". Paris: Gauthier-Villars.
51. Pontryagin, L (1946) "Topological Groups", Princeton, N.J: Princeton University Press.
52. Raimi, R A (1969) "The Peculiar Distribution of First Digits," Sci. Am. 22(6): 109-120 (December 1969).
53. Reactor Safety Study (1975) WASH 1400.
54. Savage, L J (1964) "The Foundations of Statistics Reconsidered in Studies in Subjective Probability", H E Kyburg and H Smokler (Eds), John Wiley and Sons, New York.
55. Savage, L J (1954) "The Foundations of Statistics", John Wiley and Sons, New York.
56. Savage, L J (1962)The Foundations of Statistical Inference. London: Methuen.
57. Slovic, P, Fischoff, B and Lichtenstein, S (1979) "Rating the risks", Environment 21, 14-20 and 36-39
58. Snaith, E.R. (1981) "The correlation between the predicted and the observed reliabilities of components, equipment and systems",UKAEA Report NCSR/R18.
59. Spetzler, C S and C A S Stael Von Holstein,(1975) "Probability Encoding in Decision Analysis", Manage. Sci., 22: 340-358 (November 1975).
60. Stone, M (1965) "Right Haar measure for convergence in probability to quasi-posterior distributions," Ann. Math. Statist., 36, pp. 449-453.
61. Thorne, M.C. and Williams, M.M.R (1992) "A review of expert judgement techniques will reference to nuclear safety" Progress Nucl, Energy 27, 83-254.
62. Thorne, M.C. (1993) "The use of expert opinion in formulating conceptual models of underground disposal systems and the treatment of associated bias" Reliability Engineering and System Safety 42, 161-180.
63. Van Kampen, N.G. (1981) "Stochastic Processes in Physics and Chemistry", North-Holland Pub Co.
64. Villegas, C (1977a) "On the representation of ignorance", J. Am. Stat. Assoc. 72, 651.
65. Villegas, C (1977b) "Inner Statistical Inference", J. Am. Stat. Assoc., 72(358): 453-458 (June 1977).
66. Villegas, C (1971) "On Haar Priors, in Foundations of Statistical Inference", Proceedings of the Symposium on the Foundations of Statistical Inference, University of Waterloo, Ontario, Canada, Mar 31-Apr 9, 1970, V P Godambe and D A Scott (Eds), Holt, Rinehart & Winston of Canada, Toronto.
67. Von Mises, R. (1957) "Probability, Statistics and Truth", MacMillan Co.
68. Wald, A (1950) "Statistical Decision Functions". New York: Wiley, 1950.
69. Welker, E.L. and Lipow, M. (1974) "Estimating the exponential failure rate from data with no failure events", Proc. Annual Reliability and Maintainability Symposium, Los Angeles, California.
70. Wichmann, E H (1963) "Density matrices arising from incomplete measurements," J Math. Phys. 4, pp. 884-897.
71. Wigner, E P (1959) "Group Theory". New York: Academic Press.
72. Williams, M.M.R (1994) "Review of methods of data analysis for PSA", Electrowatt Report to Health and Safety Executive.
73. Williams, M.M.R. (1994) "On the estimation of failure rates when no failures have occurred", Part I: Review of existing literature on the prediction of rare events. Electrowatt Report to Nuclear Electric.
74. Williams, M.M.R. (1994) "On the estimation of failure rates when no failures have occurred", Part II: Developments and explanation of methods used to quantify uncertainty in single components. Electrowatt Report to Nuclear Electric.
75. Winkler, R L (1967)"The Assessment of Prior Distributions in Bayesian Analysis", J. Am. Stat. Assoc., 62: 776-800.
76. Winkler, R L (1969) "Scoring Rules and the Evaluation of Probability Assessors". J. Am. Stat. Assoc., 64: 1073-1078.