The estimation of piping failure frequency is an important task to support the probabilistic risk analysis and risk-informed in-service inspection of nuclear power plant systems. This paper describes a hierarchical or two-stage Poisson-gamma Bayesian procedure and applies this to estimate the failure frequency using the Organization for Economic Co-operation and Development/Nuclear Energy Agency pipe leakage data for the United States nuclear plants. In the first stage, a generic distribution of failure rate is developed based on the failure observations from a group of similar plants. This distribution represents the interplant (plant-to-plant) variability arising from differences in construction, operation, and maintenance conditions. In the second stage, the generic prior obtained from the first stage is updated by using the data specific to a particular plant, and thus a posterior distribution of plan specific failure rate is derived. The two-stage Bayesian procedure is able to incorporate different levels of variability in a more consistent manner.
Issue Section:
Nuclear Power
1.
USNRC
, 1975, “Reactor Safety Study: An Assessment of Accident Risk in U.S. Commercial Nuclear Power Plants
,” Wash-1400, U.S. Nuclear Regulatory Commission, Washington, DC, Report No. NUREG-75/014.2.
USNRC
, 1990, “Severe Accident Risks: An Assessment for Five U.S. Nuclear Power Plants
,” U.S. Nuclear Regulatory Commission, Washington, DC, Report No. NUREG-1150.3.
Tregoning
, R.
, Abramson
, L.
, and Scott
, P.
, 2005, “Estimating Loss-of-Coolant Accident (LOCA) Frequencies Through the Elicitation Process-Draft Report for Comment
,” U.S. Nuclear Regulatory Commission, Washington, DC, Report No. NUREG-1829.4.
Atwood
, C. L.
, LaChance
, J. L.
, Martz
, H. F.
, Anderson
, D. J.
, Englehardte
, M.
, Whitehead
, D.
, and Wheeler
, T.
, 2003, “Handbook of Parameter Estimation for Probabilistic Risk Assessment
,” U.S. Nuclear Regulatory Commission, Washington, DC, Report No. NUREG/CR-6823.5.
Apostolakis
, G.
, 1978, “Probability and Risk Assessment: The Subjectivistic Viewpoint and Some Suggestions
,” Nuclear Safety
0029-5604, 19
, pp. 305
–315
.6.
Parry
, G. W.
, and Winter
, P. W.
, 1981, “Characterization and Evaluation of Uncertainty in Probabilistic Risk Analysis
,” Nuclear Safety
0029-5604, 22
, pp. 28
–42
.7.
Siu
, N. O.
, and Kelly
, D. L.
, 1998, “Bayesian Parameter Estimation in Probabilistic Risk Assessment
,” Reliab. Eng. Syst. Saf.
0951-8320, 62
, pp. 89
–116
.8.
Apostolakis
, G.
, Kaplan
, S.
, Garrick
, B. J.
, and Duphily
, R. J.
, 1980, “Data Specialization for Plant Specific Risk Studies
,” Nucl. Eng. Des.
0029-5493, 56
, pp. 321
–329
.9.
Apostolakis
, G.
, 1982, “Data Analysis in Risk Assessments
,” Nucl. Eng. Des.
0029-5493, 71
, pp. 375
–381
.10.
Vaurio
, J. K.
, 1987, “On Analytic Empirical Bayes Estimation of Failure Rates
,” Risk Anal.
0272-4332, 7
, pp. 329
–338
.11.
Kaplan
, S.
, and Garrick
, B. J.
, 1981, “On the Quantitative Definition of Risk
,” Risk Anal.
0272-4332, 1
, pp. 11
–27
.12.
Kaplan
, S.
, 1983, “On a ‘Two-Stage’ Bayesian Procedure for Determining Failure Rates From Experimental Data
,” IEEE Trans. Power Appar. Syst.
0018-9510, PAS-102
, pp. 195
–202
.13.
Fröhner
, F. H.
, 1985, “Analytic Bayesian Solution of the Two-Stage Poisson-Type Problem in Probabilistic Risk Analysis
,” Risk Anal.
0272-4332, 5
, pp. 217
–225
.14.
Fröhner
, F. H.
, 1985, “The Two-Stage Poisson-Type Problem in Probabilistic Risk Analysis
,” Risk Anal.
0272-4332, 5
, pp. 231
–234
.15.
Pörn
, K.
, 1996, “The Two-Stage Bayesian Method Used for the T-Book Application
,” Reliab. Eng. Syst. Saf.
0951-8320, 51
, pp. 169
–179
.16.
Berger
, J. O.
, 1985, Statistical Decision Theory and Bayesian Analysis
, 2nd ed., Springer-Verlag
, New York
.17.
Cooke
, R.
, Dorrepaal
, J.
, and Bedford
, T.
, 1995, “Review of SKI Data Processing Methodology
,” Delft University of Technology, SKI Report No. 95:2.18.
Meyer
, W.
, and Hennings
, W.
, 1999, “Prior Distributions in Two-Stage Bayesian Estimation of Failure Rates
,” Safety and Reliability: Proceedings of the ESREL ‘99—Tenth European Conference
, Vol. 2
, P.
Kafka
and G. I.
Schueller
, eds., Balkema
, Rotterdam, The Netherlands
, pp. 893
–898
.19.
Hora
, S. C.
, and Iman
, R. L.
, 1990, “Bayesian Modeling of Initiating Event Frequencies at Nuclear Power Plants
,” Risk Anal.
0272-4332, 10
, pp. 103
–109
.20.
Hofer
, E.
, Hora
, S. C.
, Iman
, R. L.
, and Peschke
, J.
, 1997, “On the Solution Approach for Bayesian Modeling of Initiating Event Frequencies and Failure Rates
,” Risk Anal.
0272-4332, 17
, pp. 249
–252
.21.
Hofer
, E.
, 1999, “On Two-Stage Bayesian Modeling of Initiating Event Frequencies and Failure Rates
,” Reliab. Eng. Syst. Saf.
0951-8320, 66
, pp. 97
–99
.22.
Hofer
, E.
, and Peschke
, J.
, 1999, “Bayesian Modeling of Failure Rates and Initiating Event Frequencies
,” Safety and Reliability: Proceedings of the ESREL ‘99—Tenth European Conference
, Vol. 2
, P.
Kafka
and G. I.
Schueller
, eds., Balkema
, Rotterdam, The Netherlands
, pp. 881
–886
.23.
Cooke
, R.
, Bunea
, C.
, Charitos
, T.
, and Mazzuchi
, T. A.
, 2002, “Mathematical Review of ZEDB Two-Stage Bayesian Models
,” Department of Mathematics, Delft University of Technology, Report No. 02-45.24.
Bunea
, C.
, Charitosb
, T.
, Cookec
, R. M.
, and Becker
, G.
, 2003, “Two-Stage Bayesian Models—Application to ZEDB Project
,” Safety and Reliability: Proceedings of the ESREL 2003
, T.
Bedford
and P. H. J. A. M.
van Gelder
, eds., Balkema
, Lisse, The Netherlands
, pp. 321
–331
.25.
Goel
, P. K.
, and DeGroot
, M. H.
, 1981, “Information About Hyperparameters in Hierarchical Models
,” J. Am. Stat. Assoc.
0162-1459, 76
, pp. 140
–147
.26.
Goel
, P. K.
, 1983, “Information Measure and Bayesian Hierarchical Models
,” J. Am. Stat. Assoc.
0162-1459, 78
, pp. 408
–410
.27.
Box
, G. E. P.
, and Tiao
, G. C.
, 1973, Bayesian Inference in Statistical Analysis
, Wiley
, New York
.28.
Jeffreys
, H.
, 1961, Theory of Probability
, 3rd ed., Clarendon
, Oxford
.Copyright © 2010
by American Society of Mechanical Engineers
You do not currently have access to this content.
