The objective of this study is to present a novel method of level-2 uncertainty analysis in risk assessment by means of uncertainty theory. In the proposed method, aleatory uncertainty is characterized by probability distributions, whose parameters are affected by epistemic uncertainty. These parameters are described as uncertain variables. For monotone risk models, such as fault trees or event trees, the uncertainty is propagated analytically based on the operational rules of uncertain variables. For non-monotone risk models, we propose a simulation-based method for uncertainty propagation. Three indexes, i.e., average risk, value-at-risk and bounded value-at-risk, are defined for risk-informed decision making in the level-2 uncertainty setting. Two numerical studies and an application on a real example from literature are worked out to illustrate the developed method. A comparison is made to some commonly used uncertainty analysis methods, e.g., the ones based on probability theory and evidence theory.
Uncertainty theory Uncertainty analysis Epistemic uncertainty
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This work was supported by the National Natural Science Foundation of China (Nos. 61573043, 71671009).
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Conflicts of interest
The authors declare that there is no conflict of interest regarding the publication of this paper.
Human and animal rights
This article does not contain any studies with human participants performed by any of the authors.
Apostolakis G (1990) The concept of probability in safety assessments of technological systems. Science 250(4986):1359–1364CrossRefGoogle Scholar
Aven T, Zio E (2011) Some considerations on the treatment of uncertainties in risk assessment for practical decision making. Reliab Eng Syst Saf 96(1):64–74CrossRefGoogle Scholar
Aven T, Baraldi P, Flage R, Zio E (2014) Uncertainty in risk assessment: the representation and treatment of uncertainties by probabilistic and non-probabilistic methods. Wiley, ChichesterCrossRefGoogle Scholar
Baraldi P, Zio E (2008) A combined monte carlo and possibilistic approach to uncertainty propagation in event tree analysis. Risk Anal 28(5):1309–1326CrossRefGoogle Scholar
Baraldi P, Compare M, Zio E (2013) Maintenance policy performance assessment in presence of imprecision based on dempstercshafer theory of evidence. Inf Sci 245(24):112–131zbMATHCrossRefGoogle Scholar
Helton JC, Johnson JD, Oberkampf WL, Sallaberry CJ (2010) Representation of analysis results involving aleatory and epistemic uncertainty. Int J Gen Syst 39(6):605–646MathSciNetzbMATHCrossRefGoogle Scholar
Hou Y (2014) Optimization model for uncertain statistics based on an analytic hierarchy process. Math Probl Eng 2014:1–6Google Scholar
Kang R, Zhang Q, Zeng Z, Zio E, Li X (2016) Measuring reliability under epistemic uncertainty: review on non-probabilistic reliability metrics. Chin J Aeronaut 29(3):571–579CrossRefGoogle Scholar
Ke H, Yao K (2016) Block replacement policy with uncertain lifetimes. Reliab Eng Syst Saf 148:119–124CrossRefGoogle Scholar
Kiureghian AD, Ditlevsen O (2009) Aleatory or epistemic? Does it matter? Struct Saf 31(2):105–112CrossRefGoogle Scholar
Limbourg P, Rocquigny ED (2010) Uncertainty analysis using evidence theory c confronting level-1 and level-2 approaches with data availability and computational constraints. Reliab Eng Syst Saf 95(5):550–564CrossRefGoogle Scholar
Limbourg P, Rocquigny ED, Andrianov G (2010) Accelerated uncertainty propagation in two-level probabilistic studies under monotony. Reliab Eng Syst Saf 95(9):998–1010CrossRefGoogle Scholar
Nilsen T, Aven T (2003) Models and model uncertainty in the context of risk analysis. Reliab Eng Syst Saf 79(3):309–317CrossRefGoogle Scholar
Parry GW, Winter PW (1981) Characterization and evaluation of uncertainty in probabilistic risk analysis. Nucl Saf 22:1(1):28–42Google Scholar
Pasanisi A, Keller M, Parent E (2012) Estimation of a quantity of interest in uncertainty analysis: some help from bayesian decision theory. Reliab Eng Syst Saf 100(3):93–101CrossRefGoogle Scholar
Pedroni N, Zio E (2012) Empirical comparison of methods for the hierarchical propagation of hybrid uncertainty in risk assessment in presence of dependences. Int J Uncertain Fuzziness Knowl Based Syst 20(4):509–557MathSciNetzbMATHCrossRefGoogle Scholar
Pedroni N, Zio E, Ferrario E, Pasanisi A, Couplet M (2013) Hierarchical propagation of probabilistic and non-probabilistic uncertainty in the parameters of a risk model. Comput Struct 126(2):199–213CrossRefGoogle Scholar
Ripamonti G, Lonati G, Baraldi P, Cadini F, Zio E (2013) Uncertainty propagation in a model for the estimation of the ground level concentration of dioxin/furans emitted from a waste gasification plant. Reliab Eng Syst Saf 120(6):98–105CrossRefGoogle Scholar
Shafer G (1976) A mathematical theory of evidence. Princeton University Press, PrincetonzbMATHGoogle Scholar
Tonon F (2004) Using random set theory to propagate epistemic uncertainty through a mechanical system. Reliab Eng Syst Saf 85(1):169–181CrossRefGoogle Scholar
Wang X, Peng Z (2014) Method of moments for estimating uncertainty distributions. J Uncertain Anal Appl 2(1):5CrossRefGoogle Scholar
Wang P, Zhang J, Zhai H, Qiu J (2017) A new structural reliability index based on uncertainty theory. Chin J Aeronaut 30(4):1451–1458CrossRefGoogle Scholar