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Reliability of Systems Subjected to Imperfect Fault Coverage

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Stochastic Reliability and Maintenance Modeling

Part of the book series: Springer Series in Reliability Engineering ((RELIABILITY,volume 9))

Abstract

Due to imperfect fault coverage, the reliability of redundant systems cannot be enhanced unlimitedly with the increase of redundancy. Many works have been done on the reliability modeling and optimization of systems subjected to imperfect fault coverage. The methodologies adopted mainly include combinatorial approach, ordered binary decision diagram and universal generating function. Depending on the type of fault tolerant techniques used, there are mainly three kinds of fault coverage models: (1) element level coverage (ELC). (2) fault level coverage (FLC). and (3) performance-dependent coverage (PDC). This chapter reviews the literatures on the reliability of systems subjected to imperfect fault coverage and shows an extended work.

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References

  1. Abraham JA (1979) An improved algorithm for network reliability. IEEE Trans Reliab 28(1):58–61

    Article  MathSciNet  MATH  Google Scholar 

  2. Aggarwal KK, Misra KB, Gupta JS (1975) A fast algorithm for reliability evaluation. IEEE Trans Reliab 24(1):83–85

    Article  Google Scholar 

  3. Akhtar S (1994) Reliability of k-out-of- n: G systems with imperfect fault-coverage. IEEE Trans Reliab 43(1):101–106

    Article  Google Scholar 

  4. Arnold TF (1973) The concept of coverage and its effect on the reliability model of a repairable system. IEEE Trans Comput 22(3):325–339

    Article  Google Scholar 

  5. Amari S (1997) Reliability, risk and fault-tolerance of complex systems. PhD Thesis, Indian Institute of Technology, Kharagpur

    Google Scholar 

  6. Amari SV, Dugan JB, Misra RB (1999a) A separable method for incorporating imperfect fault-coverage into combinatorial models. IEEE Trans Reliab 48(3):267–274

    Article  Google Scholar 

  7. Amari SV, Dugan JB, Misra RB (1999b) Optimal reliability of systems subject to imperfect fault-coverage. IEEE Trans Reliab 48(3):275–284

    Article  Google Scholar 

  8. Amari S, Pham H, Dill G (2004) Optimal design of k-out-of- n: G subsystems subjected to imperfect fault-coverage. IEEE Trans Reliab 53(4):567–575

    Article  Google Scholar 

  9. Bavuso SJ, Dugan JB, Trivedi KS, Rothmann EM, Smith WE (1987) Analysis of typical fault-tolerant architectures using HARP. IEEE Transactions on Reliability 36(2):176–185

    Article  Google Scholar 

  10. Bavuso SJ et al. (1994) HiRel: hybrid automated reliability predictor (HARP) integrated reliability tool system (Version 7.0), 4 vols, NASA TP 3452

    Google Scholar 

  11. Bouricius WG, Carter V, Schneider PR (1969) Reliability modeling techniques for self-repairing computer systems. In: Proceedings of the 24th national conference, ACM, pp 295–309

    Google Scholar 

  12. Bryant R (1986) Graph based algorithms for Boolean function manipulation. IEEE Trans Comput 35(8):677–691

    Article  MATH  Google Scholar 

  13. Chang YR, Suprasad VA, Kuo SY (2004) Computing system failure frequencies and reliability importance measures using OBDD. IEEE Trans Comput 53(1):2004

    Google Scholar 

  14. Chang YR, Amari SV, Kuo SY (2005) OBDD-based evaluation of reliability and importance measures for multistate systems subject to imperfect fault coverage. IEEE Trans Dependable Secure Comput 2(4):336–347

    Article  Google Scholar 

  15. Coit D, Smith A (1996) Reliability optimization of series-parallel systems using genetic algorithm. IEEE Trans Reliab 45(2):254–266

    Article  Google Scholar 

  16. Ding Y, Zuo MJ, Lisnianski A, Li W (2010) A framework for reliability approximation of multi-state weighted k-out-of- n systems. IEEE Trans Reliab 59(2):297–308

    Article  Google Scholar 

  17. Doyel SA, Dugan JB, Patterson-Hine FA (1995) A combinatorial approach to modeling imperfect coverage. IEEE Trans Reliab 44(1):87–94

    Article  Google Scholar 

  18. Dugan JB (1989) Fault trees and imperfect coverage. IEEE Transactions on Reliability 38(2):177–185

    Article  MATH  Google Scholar 

  19. Dugan JB, Trivedi KS (1989) Coverage modeling for dependability analysis of fault-tolerant systems. IEEE Transactions on Computers 38(6):775–787

    Article  Google Scholar 

  20. Dutuit Y, Rauzy A (2001) New insights in the assessment of k-out-of-n and related systems. Reliability Engineering and System Safety 72(3):303–314

    Article  Google Scholar 

  21. Huang HZ, Qu J, Zuo MJ (2009) Genetic-algorithm-based optimal apportionment of reliability and redundancy under multiple objectives. IIE Trans 41(4):287–298

    Article  Google Scholar 

  22. Kuo SY, Lu SK, Yeh FM (1999) Determining terminal-pair reliability based on edge expansion diagrams using OBDD. IEEE Trans Reliab 48(3):234–246

    Article  Google Scholar 

  23. Kuo SY, Yeh FM, Lin HY (2007) Efficient and exact reliability evaluation for networks with imperfect vertices. IEEE Trans Reliab 56(2):288–300

    Article  Google Scholar 

  24. Lee YJ, Na MG (2009) Design of delay-tolerant controller for remote control of nuclear reactor power. Nuclear Eng Technol 41(1):71–78

    Article  Google Scholar 

  25. Levitin G, Lisnianski A, Beh-Haim H, Elmakis D (1998) Redundancy optimization for series-parallel multi-state systems. IEEE Trans Reliab 47(2):165–172

    Article  Google Scholar 

  26. Levitin G (2005) Universal generating function in reliability analysis and optimization. Springer, London

    Google Scholar 

  27. Levitin G (2007) Block diagram method for analyzing multi-state systems with uncovered failures. Reliab Eng Syst Saf 92(6):727–734

    Article  Google Scholar 

  28. Levitin G (2008) Optimal structure of multi-state systems with uncovered failures. IEEE Trans Reliab 57(1):140–148

    Article  MathSciNet  Google Scholar 

  29. Levitin G, Amari SV (2008a) Multi-state systems with static performance-dependent fault coverage. Proc Inst Mech Eng, Part O J Risk Reliab 222(2):95–103

    Google Scholar 

  30. Levitin G, Amari SV (2008b) Multi-state systems with multi-fault coverage. Reliab Eng Syst Saf 93(11):1730–1739

    Article  Google Scholar 

  31. Levitin G, Xing LD (2010) Reliability and performance of multi-state systems with propagated failures having selective effect. Reliab Eng Syst Saf 95(6):655–661

    Article  Google Scholar 

  32. Li CY, Chen X, Yi XS, Tao JY (2010) Heterogeneous redundancy optimization for multi-state series-parallel systems subject to common cause failures. Reliab Eng Syst Saf 95(3):202–207

    Article  Google Scholar 

  33. Moustafa M (1997) Reliability of K-out-of- N: G systems with dependent failures and imperfect coverage. Reliab Eng Syst Saf 58(1):15–17

    Article  Google Scholar 

  34. Myers AF (2007) k-out-of- n: G system reliability with imperfect fault coverage. IEEE Trans Reliab 56(3):464–473

    Article  Google Scholar 

  35. Myers A (2008) Achievable limits on the reliability of k-out-of- n: G systems subject to imperfect fault coverage. IEEE Trans Reliab 57(2):349–354

    Article  Google Scholar 

  36. Myers A (2009) Probability of loss assessment of critical k-out-of- n: G systems having a mission abort policy. IEEE Trans Reliab 58(4):694–701

    Article  Google Scholar 

  37. Myers A, Rauzy A (2008a) Assessment of redundant systems with imperfect coverage by means of binary decision diagrams. Reliab Eng Syst Saf 93(7):1025–1035

    Article  Google Scholar 

  38. Myers A, Rauzy A (2008b) Efficient reliability assessment of redundant system subject to imperfect fault coverage using binary decision diagrams. IEEE Trans Reliab 57(2):336–348

    Article  Google Scholar 

  39. Newton J (1995) Comment on: Reliability of k-out-of- n: G systems with imperfect fault-coverage. IEEE Trans Reliab 44(1):137–138

    Article  Google Scholar 

  40. Peng R, Levitin G, Xie M, Ng SH (2011) Reliability modeling and optimization of multi-state systems with multi-fault coverage. submitted to the Seventh International Conference on mathematical methods in reliability-theory. Methods. Applications

    Google Scholar 

  41. Perhinschi MG, Napolitano MR, Campa G, Seanor B, Burken J, Larson R (2006) Design of safety monitor schemes for a fault tolerant flight control system. IEEE Trans Aerospace Electron Syst 42(2):562–571

    Article  Google Scholar 

  42. Pham H (1992a) Optimal cost-effective design of triple-modular-redundancy-with-spares systems. IEEE Transactions on Reliability 42(3):369–374

    Article  Google Scholar 

  43. Pham H (1992b) Reliability analysis of a high voltage system with dependent failures and imperfect coverage. Reliab Eng Syst Saf 37(1):25–28

    Article  Google Scholar 

  44. Pham H, Pham M (1992) Reliability analysis of dynamic redundant systems with imperfect coverage. Reliab Eng Syst Saf 35(2):173–176

    Article  MATH  Google Scholar 

  45. Schneeweiss W (1987) Approximate fault-tree analysis with prescribed accuracy. IEEE Transactions on Reliability 36(2):250–254

    Article  MathSciNet  MATH  Google Scholar 

  46. Tian ZG, Zuo MJ, Huang HZ (2008) Reliability-redundancy allocation for multi-state series-parallel systems. IEEE Trans Reliab 57(2):303–310

    Article  Google Scholar 

  47. Trivedi KS, Geist R (1983) Decomposition in reliability analysis of fault-tolerant systems. IEEE Trans Reliab 32(5):463–468

    Article  MATH  Google Scholar 

  48. Trivedi KS, Dugan JB, Geist R, Smotherman M (1984) Hybrid reliability modeling of fault-tolerant computer-systems. Comput Electr Eng 11(2–3):87–108

    Article  Google Scholar 

  49. Ushakov I (1987) Optimal standby problems and a universal generating function. Soviet J Comput Syst Sci 25(4):79–82

    MathSciNet  MATH  Google Scholar 

  50. Xing LD (2002) Analysis of generalized phased-mission system reliability, performance, and sensitivity. IEEE Trans Reliab 51(2):199–211

    Article  Google Scholar 

  51. Xing LD (2007) Reliability evaluation of phased-mission systems with imperfect fault coverage and common-cause failures. IEEE Trans Reliab 56(1):58–68

    Article  Google Scholar 

  52. Xing LD (2008) An efficient binary-decision-diagram-based approach for network reliability and sensitivity analysis. IEEE Trans Syst Man Cybern Part A Syst Humans 38(1):105–115

    Article  Google Scholar 

  53. Yeh FM, Lu SK, Kuo SY (2002) OBDD-Based evaluation of k-terminal network reliability. IEEE Trans Reliab 51(4):443–451

    Article  Google Scholar 

  54. Yeh WC (2009) A convolution universal generating function method for evaluating the symbolic one-to-all-target-subset reliability function of acyclic multi-state information networks. IEEE Trans Reliab 58(3):476–484

    Article  Google Scholar 

  55. Youssef AMA, ElMaraghy MA (2008) Performance analysis of manufacturing systems composed of modular machines using the universal generating function. J Manuf Syst 27(2):55–69

    Article  Google Scholar 

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Levitin, G., Ng, S.H., Peng, R., Xie, M. (2013). Reliability of Systems Subjected to Imperfect Fault Coverage. In: Dohi, T., Nakagawa, T. (eds) Stochastic Reliability and Maintenance Modeling. Springer Series in Reliability Engineering, vol 9. Springer, London. https://doi.org/10.1007/978-1-4471-4971-2_8

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  • DOI: https://doi.org/10.1007/978-1-4471-4971-2_8

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