Some recent advances on importance measures in reliability

IEEE Transactions on Reliability

Volumn 61, Issue 2, 2012, Pages 344-360

  Kuo, Way ^a   Zhu, Xiaoyan ^b  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b University of Tennessee   (United States)

Author keywords

Consecutive k out of n systems; joint importance measures; lifetime importance measures; reliability importance measures; structure importance measures

Indexed keywords

CONSECUTIVE-K-OUT-OF-N SYSTEM; IMPORTANCE MEASURE; INDIVIDUAL COMPONENTS; POTENTIAL APPLICATIONS; PROBABILISTIC INTERPRETATION; RELIABILITY IMPORTANCE;

RELIABILITY; SAFETY ENGINEERING;

RELIABILITY THEORY;

EID: 84861870194     PISSN: 00189529     EISSN: None     Source Type: Journal    
DOI: 10.1109/TR.2012.2194196     Document Type: Article

References (97)

1. Z. W. Birnbaum, "On the importance of different components in a multicomponent system," in Multivariate Analysis, P. R. Krishnaiah, Ed. New York: Academic Press, 1969, pp. 581-592.
2. W. S. Griffith and Z. Govindarajulu, "Consecutive -out-of-failure systems: Reliability, availability, component importance, and multistate extensions," American Journal ofMathematical and Management Sciences, vol. 5, pp. 125-160, 1985. (Pubitemid 17573465)
3. W.Kuo and X. Zhu, "Relations and generalizations of importance measures in reliability," IEEE Trans. Reliability, 2012, Accepted.
4. F. K. Hwang, "A new index of component importance," Operations Research Letters, vol. 28, pp. 75-79, 2001.
5. T. Aven and U. Jensen, Stochastic Models in Reliability. NewYork: Springer, 1999.
6. M. van der Borst and H. Schoonakker, "An overview of PSA importance measures," Reliability Engineering and System Safety, vol. 72, pp. 241-245, 2001. (Pubitemid 32498383)
7. T. Aven and T. E. Nkland, "On the use of uncertainty importance measures in reliability and risk analysis," Reliability Engineering and System Safety, vol. 95, pp. 127-133, 2010.
8. R. E. Barlowand F. Proschan, Statistical Theory of Reliability and Life Testing Probability Models. New York: Holt, Rinehart and Winston, 1975.
9. J. S. Hong and C. H. Lie, "Joint reliability-importance of two edges in an undirected network," IEEE Trans. Reliability, vol. 42, pp. 17-33, 1993.
10. M. J. Armstrong, "Joint reliability-importance of components," IEEE Trans. Reliability, vol. 44, pp. 408-412, 1995.
11. S. J. Hsu and M. C. Yuang, "Efficient computation of marginal reliability importance for reducible networks in network management," in Proceedings of the 1999 IEEE International Conference on Communications, 1999, pp. 1039-1045.
12. L. Lu and J. Jiang, "Joint failure importance for noncoherent fault trees," IEEE Trans. Reliability, vol. 56, pp. 435-443, 2007. (Pubitemid 47399752)
13. Q. Yao, X. Zhu, and W. Kuo, "Heuristics for component assignment problems based on the Birnbaum importance," IIE Trans., vol. 43, pp. 1-14, 2011.
14. Q. Yao, X. Zhu, andW. Kuo, "Importance-measure based genetic local search for component assignement problems," Annals of Operations Research, 2012, In review.
15. F. C. Meng, "Some further results on ranking the importance of system components," Reliability Engineering and System Safety, vol. 47, pp. 97-101, 1995.
16. H. S. Lee, C. H. Lie, and J. S. Hong, "A computation method for evaluating importance-measures of gates in a fault tree," IEEE Trans. Reliability, vol. 46, pp. 360-365, 1997. (Pubitemid 127762171)
17. N. D. Singpurwalla, Reliability and Risk: A Bayesian Perspective, ser. Wiley Series in Probability and Statistics. New York: John Wiley &Sons, 2006..
18. W. Kuo and M. J. Zuo, Optimal Reliability Modeling: Principles and Applications. New York: John Wiley &Sons, 2003.
19. P. J. Boland, E. El-Neweihi, and F. Proschan, "Active redundancy allocation in coherent systems," Probability in the Engineering and Informational Sciences, vol. 2, pp. 343-353, 1988.
20. P. J. Boland, E. El-Neweihi, and F. Proschan, "Redundancy importance and allocation of spares in coherent systems," Journal of Statistical Planning and Inference, vol. 29, pp. 55-65, 1991.
21. P. J. Boland, E. El-Neweihi, and F. Proschan, "Stochastic order for redundancy allocations in series and parallel systems," Advances in Applied Probability, vol. 24, pp. 161-171, 1992.
22. M. Xie and K. Shen, "On ranking of systemcomponents with respect to different improvement actions," Microelectronics and Reliability, vol. 29, pp. 159-164, 1989.
23. K. Shen and M. Xie, "On the increase of system reliability by parallel redundancy," IEEE Trans. Reliability, vol. R-39, pp. 607-611, 1990.
24. F. C. Meng, "More on optimal allocation of componenets in coherent systems," Journal of Applied Probability, vol. 33, pp. 548-556, 1996.
25. F. C. Meng, "On selecting components for redundancy in coherent systems," Reliability Engineering and System Safety, vol. 41, pp. 121-126, 1993.
26. W. E. Vesely, "A time dependent methodology for fault tree evaluation," Nuclear Engineering and Design, vol. 13, pp. 337-360, 1970.
27. J. B. Fussell, "How to hand-calculate system reliability and safety characteristics," IEEE Trans. Reliability, vol. R-24, pp. 169-174, 1975.
28. F. C. Meng, "Comparing the importance of system components by some structural characteristics," IEEE Trans. Reliability, vol. 45, pp. 59-65, 1996. (Pubitemid 126771020)
29. R. W. Youngblood, "Risk significance and safety significance," Reliability Engineering and System Safety, vol. 73, pp. 121-136, 2001. (Pubitemid 32698528)
30. H. E. Lambert, "Measure of importance of events and cut sets in fault trees," in Reliability and Fault Tree Analysis, R. E. Barlow, J. B. Fussell, and N. D. Singpurwalla, Eds. Philadelphia: Society for Industrial and Applied Mathematics, 1975, pp. 77-100.
31. B. Natvig, "A suggestion of a new measure of importance of system component," Stochastic Processes and Their Applications, vol. 9, pp. 319-330, 1979.
32. R. E. Barlow and F. Proschan, "Importance of system components and fault tree events," Statistic Processes and Their Applications, vol. 3, pp. 153-172, 1975.
33. P. J. Boland and E. El-Neweihi, "Measures of component importance in reliability theory," Computers and Operations Research, vol. 22, pp. 455-463, 1995.
34. S. Iyer, "The Barlow-Proschan importance and its generalizations with dependent components," Stochastic Processes and Their Applications, vol. 42, pp. 353-359, 1992.
35. B. Natvig, "On the reduction in remaining system lifetime due to the failure of a specific component," Journal of Applied Probability, vol. 19, pp. 642-652, 1982. (Pubitemid 13510718)
36. B. Natvig, "New light on measures of importance of system components," Scandinavian Journal of Statistics, vol. 12, pp. 43-54, 1985.
37. B. Bergman, W. J. Quirk, Ed., "On some new reliability importance measures," in Proceedings of IFAC SAFECOMP'85, 1985, pp. 61-64. (Pubitemid 16625094)
38. B. Bergman, "On reliability theory and its applications," Scandinavian Journal of Statistics, vol. 12, pp. 1-41, 1985.
39. I. Norros, "A compensator representation of multivariate life length distributions, with applications," Scandinavian Journal of Statistics, vol. 13, pp. 99-112, 1986.
40. M. Xie, "On some importance measures of system components," Stochastic Processes and Their Applications, vol. 25, pp. 273-280, 1987.
41. W. Kuo and X. Zhu, Importance Measures in Reliability, Risk, and Optimization: Principles and Applications. New York: John Wiley &Sons, 2012.
42. H. W. Chang, R. J. Chen, and F. K. Hwang, "The structural Birnbaum importance of consecutive-systems," Journal of Combinatorial Optimization, vol. 6, pp. 183-197, 2002.
43. H. W. Chang and F. K. Hwang, "Rare-event component importance for the consecutive-system," Naval Research Logistics, vol. 49, pp. 159-166, 2002.
44. P. J. Boland, F. Proschan, and Y. L. Tong, "Optimal arrangement of components via pairwise rearrangements," Naval Research Logistics, vol. 36, pp. 807-815, 1989.
45. F. C. Meng, "Comparing criticality of nodes via minimal cut (path) sets for coherent systems," Probability in the Engineering and Informational Sciences, vol. 8, pp. 79-87, 1994.
46. M. V. Koutras, G. Papadopoylos, and S. G. Papastavridis, "Note: Pairwise rearrangements in reliability structures," Naval Research Logistics, vol. 41, pp. 683-687, 1994.
47. J. Mi, "A unified way of comparing the reliaiblity of coherent systems," IEEE Trans. Reliability, vol. 52, pp. 38-43, 2003.
48. W. Kuo, V. R. Prasad, F. A. Tillman, and C.-L. Hwang, Optimal Reliability Design: Fundamentals and Applications, 2nd ed. Cambridge, UK: Cambridge University Press, 2006.
49. J. Freixas andM. Pons, "Identifying optimal components in a reliability system," IEEE Trans. Reliability, vol. 57, pp. 163-170, 2008. (Pubitemid 351454300)
50. D. A. Butler, "An importance ranking for system components based upon cuts," Operations Research, vol. 25, pp. 874-879, 1977.
51. D. A. Butler, "A complete importance ranking for components of binary coherent systems with extensions to multi-state systems," Naval Research Logistics, vol. 4, pp. 565-578, 1979.
52. F. K. Hwang, "A hierarchy of importance indices," IEEE Trans. Reliability, vol. 54, pp. 169-172, 2005. (Pubitemid 40400326)
53. X. Zhu and W. Kuo, "Comments on "A hierarchy of importance indices"," IEEE Trans. Reliability, vol. 57, pp. 529-531, 2008.
54. M. C. Cheok, G. W. Parry, and R. R. Sherry, "Use of importance measures in risk-informed regulatory applications," Reliability Engineering and System Safety, vol. 60, pp. 213-226, 1998. (Pubitemid 128393093)
55. J. N. Hagstrom, Redundancy, Substitutes and Complements in System Reliability College of Bussiness Administration, University of Illinois. Chicago, 1990, tech. rep..
56. M. J. Armstrong, "Reliability-importance and dual failure-mode components," IEEE Trans. Reliability, vol. 46, pp. 212-221, 1997. (Pubitemid 127827213)
57. J. S. Hong, H. Y. Koo, and C. H. Lie, "Joint reliability-importance of -out-of-systems," European Journal of Operational Research, vol. 142, pp. 539-547, 2002.
58. S. Jan and H.-W. Chang, "Joint reliability importance of -out-ofsystems and series-parallel systems," in Proceedings of PDPTA'06, 2006, pp. 395-398.
59. P. J. Boland and F. Proschan, "The reliability of out of systems," Annals of Probability, vol. 11, pp. 760-764, 1983.
60. J. N. Hagstrom and K. T.Mak, "System reliability analysis in the presence of dependent component failures," Probability in the Engineering and Informational Sciences, vol. 1, pp. 425-440, 1987.
61. J. S. Hong, H. Y. Koo, and C. H. Lie, "Computation of joint reliability importance of two gate events in a fault tree," Reliability Engineering and System Safety, vol. 68, pp. 1-5, 2000. (Pubitemid 30594628)
62. X. Gao, L. Cui, and J. Li, "Analysis for joint importance of components in a coherent system," European Journal of Operational Research, vol. 182, pp. 282-299, 2007. (Pubitemid 46561155)
63. E. Borgonovo and G. E. Apostolakis, "A new importance measure for risk-informed decision making," Reliability Engineering and System Safety, vol. 72, pp. 193-212, 2001. (Pubitemid 32334938)
64. E. Borgonovo, "The reliability importance of components and prime implicants in coherent and non-coherent systems including total-order interactions," European Journal of Operational Research, vol. 204, pp. 485-495, 2010.
65. M. Marseguerra and E. Zio, "Monte Carlo estimation of the differential importance measure: Application to the protection system of a nuclear reactor," Reliability Engineering and System Safety, vol. 86, pp. 11-24, 2004.
66. E. Zio and L. Podofillini, "Accounting for components interactions in the differential importance measure," Reliability Engineering and System Safety, vol. 91, pp. 1163-1174, 2006.
67. E. Borgonovo and C. Smith, "Total order reliability importance in space PSA," Procedia Social and Behavioral Sciences, vol. 2, pp. 7617-7618, 2010.
68. D. Vasseur and M. Llory, "International survey on PSA figures of merit," Reliability Engineering and System Safety, vol. 66, pp. 261-274, 1999. (Pubitemid 30531859)
69. G. Levitin, L. Podofillini, and E. Zio, "Generalised importance measures for multi-state elements based on performance level restrictions," Reliability Engineering and System Safety, vol. 82, pp. 287-298, 2003.
70. M. C. Cheok, G. W. Parry, and R. R. Sherry, "Response to "Supplemental viewpoints on the use of importance measures in risk-informed regulatory applications", " Reliability Engineering and System Safety, vol. 60, p.261-261, 1998.
71. D. T. Chiang and S. C. Niu, "Reliability of consecutive-out-of-:F system," IEEE Trans. Reliability, vol. R-30, pp. 87-89, 1981.
72. J. Shen and M. J. Zuo, "Optimal design of series consecutive-out-of-:G system with age-dependent minimal repair," Reliability Engineering and System Safety, vol. 45, pp. 277-283, 1994.
73. W.Kuo,W. Zhang, andM. J. Zuo, "Aconsecutive -out-of-:G: The mirror image of a consecutive -out-of-:F system," IEEE Trans. Reliability, vol. R-39, pp. 244-253, 1990. (Pubitemid 20714198)
74. S. Papastavridis, "The most important component in a consecutive-out-of-:F system," IEEE Trans. Reliability, vol. R-36, pp. 266-268, 1987. (Pubitemid 17614842)
75. F.-H. Lin, W. Kuo, and F. Hwang, "Structure importance of consecutive-out-of-systems," Operations Research Letters, vol. 25, pp. 101-107, 1999.
76. S. Chadjiconstantinidis and M. V. Koutras, "Measures of component importance forMarkov chain imbeddable reliability structures," Naval Research Logistics, vol. 46, pp. 613-639, 1999. (Pubitemid 30510481)
77. X. Zhu, Q. Yao, and W. Kuo, "Patterns of Birnbaum importance in linear consecutive-out-of-systems," IIE Trans., vol. 44, pp. 277-290, 2012.
78. M. J. Zuo andW. Kuo, "Reliability design for high system utilization," in Advances in Reliability and Quality Control, M. H. Hamza, Ed. Zurich: ACTA Press, 1988, pp. 53-56.
79. M. J. Zuo and W. Kuo, "Design and performance analysis of consecutive -out-of-structure," Naval Research Logistics, vol. 37, pp. 203-230, 1990. (Pubitemid 21734743)
80. R. S. Zakaria, H. A. David, and W. Kuo, "A counter-intuitive aspect of component importance measures in linear consecutive-out-ofsystems," IIE Trans., vol. 24, pp. 147-154, 1992.
81. M. J. Zuo, "Reliability and component importance of a consecutive-out-of-system," Microelectronics and Reliability, vol. 33, pp. 243-258, 1993.
82. G. J. Chang, L. Cui, and F. K. Hwang, "New comparisons in Birnbaum importance for the consecutive-out-of-system," Probability in the Engineering and Informational Sciences, vol. 13, pp. 187-192, 1999.
83. G. J. Chang, F. K. Hwang, and L. Cui, "Corrigenda on "New comparisons in Birnbaum importance for the consecutive-out-ofsystem"," Probability in the Engineering and Informational Sciences, vol. 14, p. 405, 2000.
84. F. K. Hwang, L. R. Cui, J. C. Chang, and W. D. Lin, "Comments on "Reliability and component importance of a consecutive-out-ofsystems" by Zuo," Microelectronics and Reliability, vol. 40, pp. 1061-1063, 2000.
85. H. Peng, D.W. Coit, and Q. Feng, "Component reliability criticality or importance measures for systems with degrading components," IEEE Trans. Reliability, vol. 61, pp. 4-12, 2012.
86. J. K. Vaurio, "Importance measures for multi-phase missions," Reliability Engineering and System Safety, vol. 96, pp. 230-235, 2011.
87. E. Borgonovo, "Differential, criticality and Birnbaumimportancemeasures: An application to basic event, groups and SSCs in event trees and binary decision diagrams," Reliability Engineering and System Safety, vol. 92, pp. 1458-1467, 2007. (Pubitemid 46908054)
88. N. Duflot, C. Bérenguer, L. Dieulle, and D. Vasseur, "A min cut-set-wise truncation procedure for importance measures computation in probabilistic safety assessment," Reliability Engineering and System Safety, vol. 94, pp. 1827-1837, 2009.
89. J. K. Vaurio, "Importance measures in risk-informed decision making: Ranking, optimisation and configuration control," Reliability Engineering and System Safety, vol. 96, pp. 1426-1436, 2011.
90. J. K. Vaurio, "Ideas and developments in importance measures and fault-tree techniques for reliability and risk analysis," Reliability Engineering and System Safety, vol. 95, pp. 99-107, 2010.
91. E. Borgonovo, "Epistemic uncertainty in the ranking and categorization of probabilistic safety assessmentmodel elements: Issues and findings," Risk Analysis, vol. 28, pp. 983-1001, 2008.
92. M.-H. Chun, S.-J. Han, andN.-I. Tak, "An uncertainty importancemeasure using a distance metric for the change in a cumulative distribution function," Reliability Engineering and System Safety, vol. 70, pp. 313-321, 2000.
93. C. K. Park and K. I. Ahn, "A new approach for measuring uncertainty importance and distributional sensitivity in probabilistic safety assessment," Reliability Engineering and System Safety, vol. 46, pp. 253-261, 1994.
94. E. Borgonovo, "A new uncertainty importance measure," Reliability Engineering and System Safety, vol. 92, pp. 771-784, 2007. (Pubitemid 46135960)
95. E. Borgonovo and C. Smith, "A study of interactions in the risk assessment of complex engineering systems: An application to space PSA," Operations Research, vol. 59, pp. 1461-1476, 2011.
96. S. Song, Z. Lu, and L. Cui, "A generalized Borgonovo's importance measure for fuzzy input uncertainty," Fuzzy Sets and Systems, vol. 189, pp. 53-62, 2012..
97. X. Zhu andW. Kuo, "Importancemeasures in reliability andmathematical programming," Annals of Operations Research, 2012, Accepted.