Fuzzy sets in the evaluation of reliability

Studies in Computational Intelligence

Volumn 40, Issue , 2007, Pages 363-386

  Hryniewicz, Olgierd ^a  

^a SYSTEMS RESEARCH INSTITUTE   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846152008     PISSN: 1860949X     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-37372-8_13     Document Type: Article

References (63)

1. Barlow, R., Proschan, F.: Mathematical theory of reliability, J.Wiley, New York, 1965
2. Barlow, R., Proschan, F.: Statistical theory of reliability and life testing. Probability models, Holt, Rinehart and Winston, Inc., New York, 1975
3. Birnbaum, Z.W., Esary, J.D., Saunders, S.C.: Multicomponent systems and structures, and their reliability. Technometrics 3 (1961), 55-77.
4. Cai, K.Y.: Fuzzy reliability theories. Fuzzy Sets and Systems 40 (1991), 510-511
5. Cai, K.Y.: System failure engineering and fuzzy methodology. An introductory overview. Fuzzy Sets and Systems 83 (1996), 113-133
6. Cai, K-Y., Wen C.Y., Zhang, M.L.: Fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context. Fuzzy Sets and Systems 42 (1991), 145-172
7. Cai, K-Y., Wen C.Y., Zhang, M.L.: Coherent systems in profust reliability theory. In: T. Onisawa, J. Kacprzyk (Eds.), Reliability and Safety Analyses under Fuzziness. Physica-Verlag, Heidelberg, 1995, 81-94.
8. Cappelle, B., Kerre, E.E.: Issues in possibilistic reliability theory. In: T. Onisawa, J. Kacprzyk (Eds.), Reliability and Safety Analyses under Fuzziness. Physica- Verlag, Heidelberg, 1995, 61-80.
9. Cheng, C.H.: Fuzzy repairable reliability based on fuzzy GERT. Microelectronics and Reliability 36 (1096), 1557-1563.
10. Cizelj, R.J., Mavko, B., Kljenak, I.: Component reliability assessment using quantitative and qualitative data. Reliability Engineering and System Safety 71 (2001), 81-95.
11. Cutello, V., Montero J., Yanez J.: Structure functions with fuzzy states. Fuzzy Sets and Systems 83 (1996), 189-202.
12. de Cooman, G.: On modeling possibilistic uncertainty in two-state reliability theory. Fuzzy Sets and Systems 83 (1996), 215-238
13. Dubois, D., Prade, H.: Operations on Fuzzy Numbers. Int. J. Syst. Sci. 9 (1978), 613-626.
14. Dubois, D., Prade, H.: Fuzzy real algebra. Some results. Fuzzy Sets and Systems 2 (1979), 327-348.
15. Dubois, D., Prade, H.: Fuzzy Sets and Systems. Theory and Applications. Academic Press, New York, 1980.
16. Grzegorzewski, P.: Estimation of the mean lifetime from vague data. Proceedings of the International Conference in Fuzzy Logic and Technology Eusflat 2001, Leicester, 2001, 348-351.
17. Grzegorzewski, P., Hryniewicz, O.: Testing hypotheses in fuzzy environment. Mathware and Soft Computing 4 (1997), 203-217.
18. Grzegorzewski, P., Hryniewicz, O.: Lifetime tests for vague data, In: L.A. Zadeh, J. Kacprzyk (Eds.) Computing with Words in Information/ Intelligent Systems, Part 2. Physica-Verlag, Heidelberg, 1999, 176-193.
19. Grzegorzewski, P., Hryniewicz, O.: Computing with words and life data. Int. Journ. of Appl. Math. and Comp. Sci. 13 (2002), 337-345.
20. Hryniewicz, O.: Estimation of life-time with fuzzy prior information: application in reliability. In: J.Kacprzyk, M.Fedrizzi (Eds.), Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making. Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, Berlin, 1988, 307-321.
21. Hryniewicz, O.: Lifetime tests for imprecise data and fuzzy reliability requirements, In: T. Onisawa, J. Kacprzyk (Eds.), Reliability and Safety Analyses under Fuzziness. Physica-Verlag, Heidelberg, 1995, 169-179.
22. Hryniewicz, O.: Bayes life-time tests with imprecise input information. Risk Decision and Policy 8 (2003), 1-10.
23. Hryniewicz, O.: Evaluation of reliability using shadowed sets and fuzzy lifetime data. In: K.Kolowrocki (Ed.), Advances in Safety and Reliability, vol.1. A.A.Balkema Publ., Leiden, 2005, 881-886.
24. Huang, D., Chen, T., Wang, M.J.: A fuzzy set approach for event tree analysis. Fuzzy Sets and Systems 118 (2001), 153-165.
25. Huang, H.Z., Tong, X., Zuo, M.J.: Posbist fault tree analysis of coherent systems. Reliability Engineering and System Safety 84 (2004), 141-148.
26. Jiang, Q., Chen, C.H.: A numerical algorithm of fuzzy reliability. Reliability Engineering and System Safety 80 (2003), 299-307.
27. Kruse, R.: The strong law of large numbers for fuzzy random variables. Inform. Sci. 28 (1982), 233-241.
28. Kruse, R., Meyer, K.D.: Statistics with Vague Data. D. Riedel Publishing Company, 1987.
29. Kruse, R., Meyer K.D.: Confidence intervals for the parameters of a linguistic random variable, In: J.Kacprzyk, M.Fedrizzi (Eds.), Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making. Springer-Verlag, Heidelberg, 1988, 113-123.
30. Kwakernaak, H.: Fuzzy random variables, Part I: Definitions and theorems, Inform. Sci. 15 (1978), 1-15; Part II: Algorithms and examples for the discrete case, Inform. Sci. 17 (1979), 253-278.
31. Kwakernaak, H.: Fuzzy random variables, Part II: Algorithms and examples for the discrete case, Inform. Sci. 17 (1979), 253-278.
32. Lin, C.T., Wang, M.J: Hybrid fault tree analysis using fuzzy sets. Reliability Engineering and System Safety 58 (1997), 205-213.
33. Liu, Y., Qiao, Z., Wang, G.: Fuzzy random reliability of structures based on fuzzy random variables. Fuzzy Sets and Systems 86 (1997), 345-355.
34. Misra, K.B. (Ed.): New Trends in System Reliability Evaluation. Elsevier, Amsterdam, 1993.
35. Misra, K.B., Soman K.P: Multistate fault tree analysis using fuzzy probability vectors and resolution identity. In: T. Onisawa, J. Kacprzyk (Eds.), Reliability and Safety Analyses under Fuzziness. Physica-Verlag, Heidelberg, 1995, 113-125.
36. Mizumoto, M., Tanaka, K.: Some Properties of Fuzzy Numbers. In: M.M. Gupta, R.K. Ragade., R.R. Yager (Eds.), Advances in Fuzzy Theory and Applications, North-Holland, Publ., Amsterdam, 1979, 153-164.
37. Montero, J., Cappelle, B., Kerre, E.E.: The usefulness of complete lattices in reliability theory. In: T. Onisawa, J. Kacprzyk (Eds.), Reliability and Safety Analyses under Fuzziness. Physica-Verlag, Heidelberg, 1995, 95-110.
38. Nahman, J.: Fuzzy logic based network reliability evaluation. Microelectronics and Reliability 37 (1997), 1161-1164.
39. Nishiwaki, Y.: Human factors and fuzzy set theory for safety analysis. In: M.C. Cullingford, S.M. Shah, J.H. Gittus (Eds.) Implications of Probabilistic Risk Assessment. Elsevier Applied Science, Amsterdam, 1987, 253-274.
40. Nowakowski, M.R The human operator: reliability and language of actions analysis. In: W. Karwowski, A. Mital (Eds.), Applications of Fuzzy Sets Theory in Human Factors. Elsevier, Amsterdam, 1986, 165-177.
41. Onisawa, T.: An approach to human reliability in man-machine system using error possibility. Fuzzy Sets and Systems 27 (1988), 87-103.
42. Onisawa, T.: An Application of Fuzzy Concepts to Modelling of Reliability Analysis. Fuzzy Sets and Systems 37 (1990), 120-124.
43. Onisawa, T.: System reliability from the viewpoint of evaluation and fuzzy sets theory approach. In: T. Onisawa, J. Kacprzyk (Eds.), Reliability and Safety Analyses under Fuzziness. Physica-Verlag, Heidelberg, 1995, 43-60.
44. Onisawa, T., Kacprzyk, J. (Eds.): Reliability and Safety Analyses under Fuzziness. Physica-Verlag, Heidelberg, 1995.
45. Onisawa, T., Nishiwaki, Y.: Fuzzy human reliability analysis on the Chernobyl accident. Fuzzy Sets and Systems 28 (1988), 115-127.
46. Pan, H.S., Yun, W.Y.: Fault tree analysis with fuzzy gates. Computers and Industrial Engineering 33 (1997), 569-572.
47. Pedrycz, W.: Shadowed sets: Representing and processing fuzzy sets. IEEE Trans. on Syst., Man and Cybern. Part B. Cybern. 28 (1988), 103-109.
48. Puri, M.L., Ralescu, D.A.: Fuzzy random variables. Journ. Math. Anal. Appl. 114 (1986), 409-422.
49. Rotshtein, A.: Fuzzy reliability analysis of labour (man-machine) systems. In: T. Onisawa, J. Kacprzyk (Eds.),Reliability and Safety Analyses under Fuzziness. Physica-Verlag, Heidelberg, 1995, 245-269.
50. Singer, D.: A fuzzy set approach to fault tree and reliability analysis. Fuzzy Sets and Systems 34 (1990), 145-155.
51. Suresh, P.V., Babar, A.K., Venkat Raj, V.: Uncertainty in fault tree analysis: A fuzzy approach. Fuzzy Sets and Systems 83 (1996), 135-141.
52. Tanaka, H., Fan, L.T., Lai, F.S., Toguchi, K.: Fault-tree analysis by fuzzy probability. IEEE Transactions on Reliability 32 (1983), 453-457
53. Utkin, L.V., Gurov, S.V.: Reliability of Composite Software by Different Forms of Uncertainty. Microelectronics and Reliability 36 (1996), 1459-1473.
54. Utkin, L.V., Gurov, S.V.: A general formal approach for fuzzy reliability analysis in the possibility cotext. Fuzzy Sets and Systems 83 (1996), 203-213.
55. Viertl, R.: Estimation of the reliability function using fuzzy life time data. In: P.K. Bose, S.P.Mukherjee, K.G. Ramamurthy (Eds.), Quality for Progress and Development. Wiley Eastern, New Delhi, 1989.
56. Viertl, R.: Modelling for fuzzy measurements in reliability estimation. In: V. Colombari (Ed.), Reliability Data Collection and Use in Risk and Availability Assessment. Springer Verlag, Berlin, 1989.
57. Viertl, R., Gurker, W.: Reliability Estimation based on Fuzzy Life Time Data. In: T. Onisawa, J. Kacprzyk (Eds.), Reliability and Safety Analyses under Fuzziness. Physica-Verlag, Heidelberg, 1995, 153-168.
58. Viertl, R.: Statistical Methods for Non-Precise Data. CRC Press, Boca Raton, 1996.
59. Wu, H.C.: Fuzzy Reliability Analysis Based on Closed Fuzzy Numbers. Information Sciences 103 (1997), 135-159.
60. Wu, H.C.: Fuzzy reliability estimation using Bayesian approach. Computers and Industrial Engineering 46 (2004), 467-493.
61. Wu, H.C.: Bayesian system reliability assessment under fuzzy environments. Reliability Engineering and System Safety 83 (2004), 277-286.
62. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning, Parts 1, 2, and 3. Information Sciences 8 (1975), 199-249, 301-357, 9 (1975), 43-80.
63. Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1 (1978), 3-28.