Overcoming the uncertainty in a research reactor LOCA in level-1 PSA; Fuzzy based fault-tree/event-tree analysis

Document Type: Original Manuscript


1 Department of Mechanical Engineering, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran

2 Department of Nuclear Engineering, Faculty of New Sciences and Technologies, University of Isfahan, Isfahan, Iran



Probabilistic safety assessment (PSA) which plays a crucial role in risk evaluation is a quantitative approach intended to demonstrate how a nuclear reactor meets the safety margins as part of the licensing process. Despite PSA merits, some shortcomings associated with the final results exist. Conventional PSA uses crisp values to represent the failure probabilities of basic events. This causes a high level of uncertainty due to the inherent imprecision and vagueness of failure input data. In this paper, to tackle this imperfection, a fuzzy approach is employed with fault tree analysis and event tree analysis. Thus, instead of using the crisp values, a set of fuzzy numbers is applied as failure probabilities of basic events. Hence, in the fault tree and event tree analysis, the top events and the end-states frequencies are treated as fuzzy numbers. By introducing some fuzzy importance measures the critical components which contribute maximum to the system failure and total uncertainty are identified. As a practical example, under redesign Iranian heavy water research reactor loss of coolant accident is studied. The results show that the reactor protection system has the largest index in sequences lead to a core meltdown. In addition, the emergency core cooling system has a main role in preventing abnormal conditions.

Graphical Abstract

Overcoming the uncertainty in a research reactor LOCA in level-1 PSA; Fuzzy based fault-tree/event-tree analysis


  • Fuzzy approach applied to a heavy water research reactor LOCA for risk analysis.
  • The fault trees of all safety systems and the fuzzy event tree were developed.
  • The emergency core cooling system has a main role in preventing abnormal conditions.


Aldemir, T. (2013). A survey of dynamic  methodologies for probabilistic safety assessment of nuclear power plants, Annals of Nuclear Energy 52:113–124.

Ferdous, R., Khan, F., Sadiq, R., Amyotte, P., & Veitch, B. (2001). Fault and Event Tree Analyses for Process Systems Risk Analysis: Uncertainty Handling Formulations. Risk Analysis 31(1): 86-107.

Guimarães, A.C.F., Lapa, C.M.F., & Moreira, M.L. (2011a). Fuzzy methodology applied to Probabilistic Safety Assessment for digital system in nuclear power plants, Nuclear Engineering and Design 241:3967– 3976.

Guimarães, A.C.F., Lapa, C.M.F., Simões Filho, F.F.L., & Cabral, D.C. (2011b) Fuzzy uncertainty modeling applied to AP1000 nuclear power plant LOCA. Annals of Nuclear Energy 38(8):1775-1786.

Gupta, S., Bhattacharya, J. (2007). Reliability analysis of a conveyor system using hybrid data. Qual Reliab Eng Int 23(7):867.

Hasannejad, H., Seyyedi, S.M., & Hashemi-Tilehnoee, M. (2019). Utilizing an auxiliary portable lube oil heating system in Aliabad Katoul-Iran V94. 2 gas turbine during standstill mode: a case study. Propulsion and Power Research. 8(4):320-328.

Hashemi-Tilehnoee, M., Pazirandeh, A., & Tashakor, S. (2010). HAZOP-study on heavy water research reactor primary cooling system. Annals of Nuclear Energy 37:428–433.

Hryniewicz, O. (2007). Fuzzy Sets in the Evaluation of Reliability. In: Levitin, G. (Editor). Computational Intelligence in Reliability Engineering. New Metaheuristics, Neural and Fuzzy Techniques in Reliability. Springer-Verlag. Berlin Heidelberg. pp. 363-386.

Huang, D., Chen, T., & Wang, M.J.J. (2001). A fuzzy set approach for event tree analysis, Fuzzy Sets and Systems 118:153-165.

IAEA-International Atomic Energy Agency (1992) Procedure for conducting probabilistic safety assessment of nuclear power plants (level 1). Safety series no. 50-P-4. Vienna.

IAEA-TECDOC-930 (1997) Generic component reliability data for research reactor PSA. Vienna: International Atomic Energy Agency.

 IAEA-TECDOC-478 (1998) Component reliability data for use in probabilistic safety assessment. Vienna:  International Atomic Energy Agency.

Kančev, D., Čepin, M., & Gjorgiev, B. (2014). Development and application of a living probabilistic safety assessment tool: Multi-objective multi-dimensional optimization of surveillance requirements in NPPs considering their ageing, Reliability Engineering and System Safety131:135–147.

Keller, M., & Modarres, M. (2005). A historical overview of probabilistic risk assessment development and its use in the nuclear power industry: a tribute to the late professor Norman Carl Rassmussen. Reliability Engineering & System Safety 89:271-285.

Klir, G.J., & Folger, T.A. (1988). Fuzzy Sets, Uncertainty and Information. Prentice Hall; 1st  Edition; ISBN 13: 978-0133459845.

Lee, W.S., Grosh, D.L., Tillman, F.A., & Lie, C.H. (1985). Fault tree analysis, methods, and applications-a review. IEEE Reliab Trans R-34:194-203.

Lee, J., & McCormick, N. (2012). Risk and Safety Analysis of Nuclear Systems, 1st  edition. Wiley, ISBN-13: 978-0470907566.

Liang, G., & Wang, M. (1993). Evaluating human reliability using fuzzy relation. Microelectronics Reliability 33(1): 63–80.

Mahmood, Y.A., Ahmadi, A., Verma, A.K., Srividya, A., Kumar, U. (2013). Fuzzy fault tree analysis: a review of concept and application, Int J Syst Assur Eng Manag 4(1):19–32.

Markowski, A., & Mannan, M. (2008). Fuzzy risk matrix. Journal of Hazardous Materials159(1): 152-157.

Martorell, S., Carlos, A., Sanchez, A., & Serradell, V. (2000). Constrained optimization of test intervals using steady-state genetic algorithm. Reliability Engineering and System Safety 67: 215-232.

Miller, G. (1956). The magical number seven, plus or minus two: Some limits on our capacity for processing information. The psychological review 63:81-97.

Misra, K.B., Weber, G.G. (1990). Use of fuzzy set theory for level-I studies in probabilistic risk assessment, Fuzzy Sets and Systems 37:139-160.

Modarres, M., Kaminskiy, M.P., & Krivtsov, V. (2009). Reliability Engineering and Risk Analysis: A Practical Guide. CRC Press; 2nd Ed 2009. ISBN-13: 978-0849392474.

Onisawa T (1988) An approach to human reliability in man-machine systems using error possibility. Fuzzy Sets and Systems 27(2): 87-103.

Onisawa ,T. (1989). Fuzzy theory in reliability analysis. Fuzzy Sets Syst 30(3):361–363.

Onisawa T (1990) An application of fuzzy concepts to modelling of reliability analysis. Fuzzy Sets and Systems 37(3): 267-286.

Purba, J.H., Lu, J., Ruan, D., & Zhang, G. (2012). An area defuzzification technique to assess nuclear event reliability data from failure possibilities. International Journal of Computational Intelligence and Applications11(4): 1250022.

Purba, J.H., Lu, J., Zhang, G. (2014). An intelligent system by fuzzy reliability algorithm in fault tree analysis for nuclear power plant probabilistic safety assessment, International Journal of Computational Intelligence and Applications 13(3):1450017.

Purba, J.H. (2014a). Fuzzy probability on reliability study of nuclear power plant probabilistic safety assessment: A review, Progress in Nuclear Energy 76:73-80.

Purba, J.H. (2014b). A fuzzy-based reliability approach to evaluate basic events of fault tree analysis for nuclear power plant probabilistic safety assessment, Annals of Nuclear Energy 70:21–29.

Purba, J.H., Lu, J., Zhang, G., & Pedrycz, W. (2014). A fuzzy reliability assessment of basic events of fault trees through qualitative data processing. Fuzzy Sets and Systems 243:50-69.

Purba, J.H., Tjahyani, D.T.S., Ekariansyah, A.S., & Tjahjono, H. (2015). Fuzzy probability based fault tree analysis to propagate and quantify epistemic uncertainty, Annals of Nuclear Energy 85:1189–1199.

Rao K.D., Kushwaha, H.S., Verma, A.K., & Srividya, A. (2007). Quantification of epistemic and aleatory uncertainties in level-1 probabilistic safety assessment studies, Reliability Engineering and System Safety 92: 947–956.

Ross, T.J. (2004). Development of Membership Functions. In: Fuzzy Logic with Engineering Applications. John Wiley & Sons, pp. 197-212.

Wolkenhauer, O. (2001). Fuzzy mathematics. In: Data Engineering: Fuzzy Mathematics in Systems Theory and Data Analysis. John Wiley & Sons, pp. 197-212.

Woo, T.H., Noh, S.W., Kim, T.W., Kang,  K.M., & Kim, Y.I. (2014). A fuzzy set safety assessment for a core falling failure accident (CFFA) in a spherical isotropic power reactor (SIPR), Energy Sources, Part A, 36:2338–2346.

Zadeh, L.A. (1965). Fuzzy sets. Information and control 8(3): 338–353.

Zimmmermann, H.J., (1991). Fuzzy set theory and its applications, 2nd. Ed, Kluwer academic publishers, Boston.