A top-down iteration algorithm for Monte Carlo method for probability estimation of a fault tree with circular logic

  • Han, Sang Hoon (Risk & Environmental Safety Research Division, Korea Atomic Energy Research Institute)
  • Received : 2017.12.28
  • Accepted : 2018.04.02
  • Published : 2018.08.25


Calculating minimal cut sets is a typical quantification method used to evaluate the top event probability for a fault tree. If minimal cut sets cannot be calculated or if the accuracy of the quantification result is in doubt, the Monte Carlo method can provide an alternative for fault tree quantification. The Monte Carlo method for fault tree quantification tends to take a long time because it repeats the calculation for a large number of samples. Herein, proposal is made to improve the quantification algorithm of a fault tree with circular logic. We developed a top-down iteration algorithm that combines the characteristics of the top-down approach and the iteration approach, thereby reducing the computation time of the Monte Carlo method.


Supported by : National Research Foundation of Korea (NRF)


  1. Fault Tree Handbook, U.S. Nuclear Regulatory Commission, NUREG-0492, 1981.
  2. A. Rauzy, New algorithms for fault trees analysis, Reliability Engineering and System Safety 40 (1993) 203-211.
  3. H. Kumamoto, 1980. Dagger-sampling Monte Carlo for system unavailability evaluation, IEEE Transactions on Reliability R 29 (2) (1980) 122-125.
  4. Sang Hoon Han, Jin Hee Park, Dong San Kim, Ho-Gon Lim, Seung Cheol Jang, Comparison of Various Methods to Quantify a Fault Tree for Seismic PSA, Transactions of the Korean Nuclear Society Spring Meeting, Jeju, Korea, 2015. May 7-8.
  5. Sang Hoon Han, Ho-Gon Lim, Top event probability evaluation of a fault tree having circular logics by using Monte Carlo method, Nuclear Engineering and Design 243 (2012) 336-340.
  6. Joon-Eon Yang, Sang-Hoon Han, Jin-Hee Park, Young-Ho Jin, Analytic method to break logical loops automatically in PSA, Reliability Engineering and System Safety 56 (1997) 101-105.
  7. A Study for Nuclear Safety Improvement - Improvement of Level 1 PSA Computer Code Package, KAERI, KAERI/RR-1487/94, 1995.
  8. Jussi K. Vaurio, A recursive method for breaking complex logic loops in Boolean system models, Reliability Engineering and System Safety 92 (2007) 1473-1475.
  9. FTeMC Quick Guide, Fault Tree Top Event Probability Evaluation Using Monte Carlo Simulation, KAERI, KAERI-ISA-memo-FTeMC-01, Rev. 1, 2017.
  10. Addenda to ASME/ANS RA-S-2008 Standard for Level 1/Large Early Release Frequency Probabilistic Risk Assessment for Nuclear Power Plant Applications, ASME/ANS RA-Sb-2013, The American Society of Mechanical Engineers, 2013.