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A Risk-Uncertainty Formula Accounting for Uncertainties of Failure Probability and Consequence in a Nuclear Powerplant



Jeffrey T. Fong, Stephen R. Gosselin, Pedro V. Marcal, James J. Filliben, Nathanael A. Heckert, Robert E. Chapman


This paper is a continuation of a recent ASME Conference paper entitled "Design of a Python-Based Plug-in for Bench-marking Probabilistic Fracture Mechanics Computer Codes with Failure Event Data" (PVP2009-77974). In that paper, which was co-authored by Fong, deWit, Marcal, Filliben, Heckert, and Gosselin, we designed a probability-uncertainty plug-in to automate the estimation of leakage probability with uncertainty bounds due to variability in a large number of factors. The estimation algorithm was based on a two-level full or fractional factorial design of experiments such that the total number of simulations will be small as compared to a Monte-Carlo method. This feature is attractive if the simulations were based on finite element analysis with a large number of nodes and elements. In this paper, we go one step further to derive a risk-uncertainty formula by computing separately the probability-uncertainty and the consequence-uncertainty of a given failure event, and then using the classical theory of error propagation to compute the risk-uncertainty within the domain of validity of that theory. The estimation of the consequence-uncertainty is accomplished by using a public-domain software package entitled "Cost-Effectiveness Tool for Capital Asset Protection, version 4.0, 2008" ( or NIST Report NISTIR-7524), and is more fully described in a companion paper entitled "An Economics-based Intelligence (EI) Tool for Pressure Vessels & Piping (PVP) Failure Consequence Estimation," (PVP2010-25226, Session MF-23.4 of this conference). A numerical example of an application of the risk-uncertainty formula using a 16-year historical database of probability and consequence of main steam and hot reheat piping systems is presented. Implication of this risk-uncertainty estimation tool to the design of a risk-informed in-service inspection program is discussed.
Proceedings Title
Proceedings of the ASME Pressure Vessels and Piping Conference
Conference Dates
July 18-22, 2010
Conference Location
Bellevue, WA


ASME B&PV Code, error propagation, failure consequence, failure probability, nuclear power plant, probabilistic risk assessment, risk uncertainty formula


Fong, J. , R., S. , Marcal, P. , Filliben, J. , Heckert, N. and Chapman, R. (2010), A Risk-Uncertainty Formula Accounting for Uncertainties of Failure Probability and Consequence in a Nuclear Powerplant, Proceedings of the ASME Pressure Vessels and Piping Conference, Bellevue, WA, [online], (Accessed June 13, 2024)


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Created July 20, 2010, Updated February 19, 2017