Fuzzy system reliability using intuitionistic fuzzy Weibull lifetime distribution

  • Kumar, Pawan (Department of Mathematics, Statistics & Computer Science, G. B. Pant University of Agriculture & Technology) ;
  • Singh, S.B. (Department of Mathematics, Statistics & Computer Science, G. B. Pant University of Agriculture & Technology)
  • Received : 2014.08.04
  • Accepted : 2015.05.27
  • Published : 2015.06.30

Abstract

Present study investigates the fuzzy reliability of some systems using intuitionistic fuzzy Weibull lifetime distribution, in which the lifetime parameters are assumed to be fuzzy parameter due to uncertainty and inaccuracy of data. Expressions for fuzzy reliability, fuzzy mean time to failure, fuzzy hazard function and their ${\alpha}$-cut have been discussed when systems follow intuitionistic fuzzy Weibull lifetime distribution. A numerical example is also taken to illustrate the methodology to calculate the fuzzy reliability characteristics of systems.

Keywords

References

  1. Atanassov, K. (1986). Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3
  2. Baloui Jamkhaneh, E. (2011). An evaluation of the systems reliability using fuzzy lifetime distribution,Journal of Applied Mathematics, Islamic Azad University of Lahijan, 7, 73-80.
  3. Baloui Jamkhaneh, E. (2012). Reliability estimation under the fuzzy environments, 140804 The Journal of Mathematics and Computer Science, 5, 28-39.
  4. Baloui Jamkhaneh, E. (2013). Analyzing system reliability using fuzzy Weibull lifetime distribution, International Journal of Applied Operational Research, 4, 93-102.
  5. Cai, K. Y. and Zhang, M. L. (1995). Coherent systems in profust reliability theory, in: T. Onisawa, J. Kacprzyk (Eds.),Reliability and Safety analyzes under fuzziness, Physica-Verlag, Heidelberg, 81-94.
  6. Chen, S.M. (1994). Fuzzy system reliability analysis using fuzzy number arithmetic operations, Fuzzy Sets and Systems, 64, 31-38. https://doi.org/10.1016/0165-0114(94)90004-3
  7. Chen, S.M. (2003). Analyzing fuzzy system reliability using vague set theory, International Journal of Applied Science and Engineering, 1,82-88.
  8. De, S. K., Biswas, R. and Roy, A. R. (2001).Some operations on intuitionistic fuzzy sets,FuzzySets and Systems, 114, 477-484.
  9. Mahapatra, G. S. (2009). Reliability evaluation using triangular intuitionistic fuzzy numbers arithmetic operations, World Academy of Science, Engineering and Technology, 50, 574-580.
  10. Sharma, M. K. (2012). Reliability analysis of a system using intuitionistic fuzzy sets, International Journal of Soft Computing and Engineering, 2, 431-440.
  11. Singer, D. (1990). A fuzzy set approach to fault tree and reliability analysis. Fuzzy Sets and Systems, 34, 145-55. https://doi.org/10.1016/0165-0114(90)90154-X
  12. Utkin, L.V. and Grouv, S.V. (1999). Imprecise reliability models for the general lifetime distribution classes, 1st International Symposium on Imprecise Probabilities and Their Application, Ghent, Belgium.
  13. Zadeh, L. A. (1965). Fuzzy sets, Information and Control, 8, 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X