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.

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
.
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