Causes of Uncertainty in FTA Method and Use of Fuzzy Logic to Solve This Problem


Nowadays increasing the number of chemical industries leads to more industrial accidents. Due to consequences of accidents imposed high costs to industry, society and environment. This makes safety analysis more important. Therefore qualitative and quantitative hazard analyses are essential for identification and quantification of hazards. Fault tree analysis (FTA) is an established technique in hazard identification. People when using FTA often suffers from a lack of detailed data on failure rates, uncertainties in available data, imprecision and vagueness. This may lead to uncertainty in results and process risk level. Fuzzy logic deals with uncertainty and imprecision, and is an efficient tool for solving problems where knowledge of uncertainty may occur. In this paper traditional FTA was combined with fuzzy set theory. In fuzzy method, all variables are replaced by fuzzy numbers in the process of fuzzification and subsequently fuzzy probability of the top event is used for fault tree.

Keywords: Fault Tree Analysis, Uncertainty, Fuzzy Logic, Fuzzy Operator.

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  • M. Stamatelatos, NASA HQ, OSMA, Fault Tree Handbook with Aerospace Applications, NASA Office of Safety and Mission Assurance NASA Headquarters, Washington, DC, 2002.
  • D. Dubois, Francesc Esteva, Llu´ıs Godo, Henri Prade, Fuzzy-Set based logics – a history-oriented presentation of their main developments, Handbook of the History of Logic, Volume 8, Elsevier, 2007.
  • H. Tanaka, L.T. Fan, F.S. Lai and K.Toguchi, Fault-tree analysis by fuzzy probability. IEEE Trans. Reliability, Vol. 32, pp. 453-457, 1983.
  • H. Furuta and N.Shiraishi. Fuzzy importance in fault tree analysis. Fuzzy Sets and Systems, Vol. 12, pp. 205-213, 1984.
  • W. Karwowski and A. Mital, Potential application of fuzzy sets in industrial safety engineering, Fuzzy Sets and Systems, 19, 105–120, 1986.
  • D. Singer, A fuzzy set approach to fault tree analysis, Fuzzy Sets and Systems 34, pp.145-155, 1990.
  • D. Singer, Fault tree analysis based on fuzzy logic, Computers & Chemical Engineering, Vol. 14, No. 3, PP. 259-264, 1990.
  • C. Ching-Hsue and M. Don-Lin, Fuzzy system reliability analysis of confidence, Fuzzy Sets and Systems, 56, pp. 29-35, 1993.
  • L. Ching-Torng and J. W. Mao-Jiun, Hybrid fault tree analysis using fuzzy sets, Reliability Engineering and System Safety, 58, pp.205-213, 1997.
  • O. Takehisa, An approach to human reliability in man-machine systems using error possibility, Fuzzy sets and systems, 27, pp.87-103, 1988.
  • H. Hong-Zhong, T. Xin , Ming J. Zuo, Posbist fault tree analysis of coherent systems, Reliability Engineering and System Safety, 84, pp. 141–148, 2004.
  • Y. Dong, D. Yu, Estimation of failure probability of oil and gas transmission pipelines by fuzzy fault tree analysis, Journal of Loss Prevention in the Process Industries, 18, pp. 83–88, 2005.
  • H. Li-Ping He, H. Hong-Zhong,Ming J. Zuo, Fault Tree Analysis Based on Fuzzy Logic, IEEETrans, Reliability,pp. 453-457, 2007.
  • S. Adam, a. Markowski, M. Sam Mannan b, B. Agata,Fuzzy logic for process safety analysis, Journal of Loss Prevention in the Process Industries, 22, pp.695–702, 2009.
  • L. Yanfeng, H. Hong-Zhong, Z. Shun-peng, L. Yu, An application of fuzzy fault tree analysis to un contained events of an Areo- engine Rotor, Int.J. Turbo Jet-Engines, 29, pp. 309-315, 2012.
  • L.A. Zadeh, Fuzzy sets: Information and control, Vol. 8, pp. 338-353, 1965.
  • Johen B. Bowles, Colon E. Pelaez, Application of Fuzzy Logic to Reliability Engineering,Proceeding of the IEEE, VOL. 83, and NO. 3, pp.435-449, 1994.
  • A. Aydin, Fuzzy set approaches to classification of rock masses, Engineering Geology, 74, Issues 3-4, pp. 227-245, 2004.
  • H. Nasseri, Fuzzy Numbers: Positive and Nonnegative, International Mathematical Forum, 3, no. 36, pp.1777 – 1780, 2008.