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

Abstract

This paper is a continuation of a recent ASME Conference paper entitled “Design of a Python-Based Plug-in for Benchmarking 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” (http://www.bfrl.nist.gov/oae/ 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.

Composite Material Property Database Using Smooth Specimens to Generate Design Allowables With Uncertainty Estimation

“…The statistical analysis performed in this work was based on the software Dataplot from NIST (National Institute of Standards and Technology) [22,23,24]. Dataplot is a multiplatform software for scientific visualization, statistical analysis and non-linear modeling.…”

A New Approach to Finding a Risk-Informed Safety Factor for “Fail-Safe” Pressure Vessel and Piping Design

“…Statistically speaking, this approach yields a failure probability equal to the sum of 0.05 (due to the 95 % confidence level) and 0.01 (due to the 99 % coverage), or, 0.06. A review of the literature on engineering risk analysis and system reliability (see, e.g., [8][9][10][11][12][13][14]), shows that the combination of the 95 % confidence level and the 99 % coverage, or, the A-basis design allowable for a critical aircraft part, is not conservative enough for a "fail-safe" design. For example, a 99 % coverage of the surface of a Boeing 787 fuselage and wings, estimated to be about 4,000 square meters using data reported by Norris and Wagner [15], will miss 40 square meters of area that may fail no matter which distribution is assumed to fit the UTS data.…”