Two-unit repairable systems with common-cause shock failures and fuzzy parameters: Parametric programming approach

International Journal of Systems Science

Volumn 39, Issue 5, 2008, Pages 449-459

  Huang, Hsin I ^a   Lin, Chuen Horng ^a   Ke, Jau Chuan ^a  

^a NATIONAL TAICHUNG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Taiwan)

Author keywords

Availability; Fuzzy sets; Mathematical programming; Mean time to failure; Shock failures

Indexed keywords

FAILURE ANALYSIS; FUZZY SETS; INFORMATION USE; MEMBERSHIP FUNCTIONS; NONLINEAR PROGRAMMING;

MEAN TIME TO FAILURE; SHOCK FAILURES;

SYSTEMS ENGINEERING;

EID: 40849135795     PISSN: 00207721     EISSN: 14645319     Source Type: Journal    
DOI: 10.1080/00207720701778445     Document Type: Article

References (40)

1. G.E. Apostolakis, "The effect of a certain class of potential common mode failures on the reliability of redundant systems", Nucl. Eng. Des., 36, pp. 123-133, 1976.
2. R. Billinton and R.N. Allen, Reliability Evaluation of Engineering Systems: Concepts and Techniques, New York: Plenum., 1983.
3. R. Billinton and J. Pan, "Optimal maintenance scheduling in a two identical component parallel redundant system", Reliab. Eng. Syst. Safe., 59, pp. 309-316, 1998.
4. K.Y. Cai, C.Y. Wen and M.L. Zhang, "Fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context", Fuzzy Set. Syst., 42, pp. 145-172, 1991a.
5. K.Y. Cai, C.Y. Wen and M.L. Zhang, "Posbist reliability behavior of typical system with two types of failures", Fuzzy Set. Syst., 43, pp. 17-32, 1991b.
6. K.Y. Cai, C.Y. Wen and. W.L. Zhang, "Fuzzy states as a basis for a theory of fuzzy reliability", Microelectron. Reliab., 33, pp. 2253-2263, 1993.
7. K.Y. Cai, C.Y., Wen and M.L. Zhang, "Posbist reliability behavior of fault-tolerant systems", Microelectron. Reliab., 35, pp. 49-56, 1995.
8. D.I. Cleland and D.F. Kocaoglu, Engineering Management, New York: McGraw-Hill, 1981.
9. A.T. de Almeida and F.M. Campello de Souza, "Decision theory in maintenance strategy for a 2-unit redundant standby system", IEEE Trans. Reliab., 42, pp. 401-407, 1993.
10. P. Fortemps and M. Roubens, "Ranking and defuzzification methods based on area compensation", Fuzzy Set. Syst., 82, pp. 319-330, 1996.
11. T. Gal, Postoptimal Analysis, Parametric Programming, and Related Topics, New York: McGraw-Hill, 1979.
12. J. Gasemyr and B. Natvig, "The posterior distribution of the parameters of component lifetimes based on autopsy data in a shock model", Scandinavian J. Stat., 25, pp. 271-292, 1998.
13. L.R. Goel and P. Shrivastava, "Profit analysis of a two-unit redundant system, with provision for test and correlated failures and repairs", Microelectron. Reliab., 31, pp. 827-833, 1991.
14. M. Gururajan and B. Srinivasan, "A. complex two-unit system, with random breakdown of repair facility", Microelectron. Reliab., 35, pp. 299-302, 1995.
15. C.A. Holloway, Decision Making Under Uncertainly: Models and Choices, Englewood Cliffs, NJ: Prentice-Hall, 1979.
16. M. Jain and R.P. Ghimire, "Reliability of k-r-out-of-N: G system subject to random and common-cause failure", Perform. Evaluation, 29, pp. 213-218, 1997.
17. Q. Jiang and C.-H. Chen, "A numerical algorithm of fuzzy reliability", Reliab. Eng. Syst. Safe., 80, pp. 299-307, 2003.
18. A. Kaufmann, Introduction to the Theory of Fuzzy Subsets, Vol. 1, New York: Academic Press, 1975.
19. S. Kotz, C.D. Lai and M. Xie, "On the effect of redundancy for systems with dependent components", HE Trans., 35, pp. 1103-1110, 2003.
20. P.H. Kvam and J.G. Miller, "Common-cause failure prediction using data mapping. Reliability", Eng. Syst. Safe., 76, pp. 273-278, 2002a.
21. P.H. Kvam and J.G. Miller, "Discrete predictive analysis in probability safety assessment", J. Quality Tech., 34, pp. 106-117, 2002b.
22. T. Onisawa, "Fuzzy theory in reliability analysis", Fuzzy Set. Syst., 29, pp. 250-251, 1989.
23. S. Osaki and T. Nakagawa, "Bibliography for reliability and availability of stochastic systems", IEEE Trans. Reliab., 25, pp. 284-287, 1976.
24. H.M. Prade, "An outline of fuzzy or possibilistic models for queueing systems," in Fuzzy Sets P.P. Wang and S.K. Chang (Eds), New York: Plenum. Press, 1980.
25. S.P. Rajamanickam and B. Chandrasekar, "Reliability measures for two-unit systems with a dependent structure for failure and repair times", Microelectron. Reliab., 37, pp. 829-833, 1997.
26. J.H. Seo, J.S. Jang and D.S. Bai, "Lifetime and reliability estimation of repairable redundant system subject to periodic alternation", Reliab. Eng. Syst. Safe., 80, pp. 197-204, 2003.
27. S.K. Srinivasan and R. Subramanian, Probabilistic Analysis of Redundant Systems, Vol. 175, Berlin: Springer Verlag, 1980.
28. K.S. Trivedi, Probability and Statistics with Reliability, Queueing and Computer Science Applications, 2nd ed., New York: John Wiley & Sons, 2002.
29. L.V. Utkin, "Knowledge based fuzzy reliability assessment", Microelectron. Reliab., 34, pp. 863-874, 1994a.
30. L.V. Utkin, "Fuzzy reliability of repairable systems in the possibility context", Microelectron. Reliab., 34, pp. 1865-1876, 1994b.
31. J.K. Vaurio, "The probabilistic modeling of external, common-cause shocks in redundant systems", Reliab. Eng. Syst. Safe., 50, pp. 97-107, 1995.
32. J.K. Vaurio, "An implicit method for incorporating common-cause failures in system analysis", IEEE Trans. Reliab., 47, pp. 173-179, 1998.
33. J.K. Vaurio, "Extensions of the uncertainty quantification of common-cause failure rates", Reliab. Eng. Syst. Safe., 78, pp. 63-69, 2002.
34. K.-H. Wang, Y.-J. Liou and W.L. Pearn, "Cost benefit analysis of series systems with warm standby components and general repair times", Math. Methods Oper. Res., 61, pp. 329-343, 2005.
35. H.-C. Wu, "Fuzzy reliability analysis based on closed fuzzy numbers", Inform. Sci., 103, pp. 35-159, 1997.
36. V.S.S. Yadavalli, M. Botha and A. Bekker, "Asymptotic confidence limits for the steady-state availability of a two-unit parallel system with preparation time for the repair facility", Asia-Pacific J. Oper. Res., 19, pp. 249-256, 2005.
37. V.S.S. Yadavalli, A. Bekker and J. Pauw, "Bayesian study of a two-component system with common-cause shock failures", Asia-Pacific J. Oper.Res., 22, pp. 105-119, 2005.
38. R. R. Yager, "A. procedure for ordering fuzzy subsets of the unit interval", Inform. Sci., 24, pp. 143-161, 1981.
39. L.A. Zadeh, "Fuzzy sets as a basis for a theory of possibility", Fuzzy Set. Syst., 1, pp. 3-28, 1978.
40. H.J. Zimmermann, Fuzzy Set Theory and Its Applications, 4th ed., Boston: Kluwer Academic, 2001.