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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abraham JA (1979) An improved algorithm for network reliability. IEEE Trans Reliab 28(1):58–61
Aggarwal KK, Misra KB, Gupta JS (1975) A fast algorithm for reliability evaluation. IEEE Trans Reliab 24(1):83–85
Akhtar S (1994) Reliability of k-out-of- n: G systems with imperfect fault-coverage. IEEE Trans Reliab 43(1):101–106
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
Amari S (1997) Reliability, risk and fault-tolerance of complex systems. PhD Thesis, Indian Institute of Technology, Kharagpur
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
Amari SV, Dugan JB, Misra RB (1999b) Optimal reliability of systems subject to imperfect fault-coverage. IEEE Trans Reliab 48(3):275–284
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
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
Bavuso SJ et al. (1994) HiRel: hybrid automated reliability predictor (HARP) integrated reliability tool system (Version 7.0), 4 vols, NASA TP 3452
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
Bryant R (1986) Graph based algorithms for Boolean function manipulation. IEEE Trans Comput 35(8):677–691
Chang YR, Suprasad VA, Kuo SY (2004) Computing system failure frequencies and reliability importance measures using OBDD. IEEE Trans Comput 53(1):2004
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
Coit D, Smith A (1996) Reliability optimization of series-parallel systems using genetic algorithm. IEEE Trans Reliab 45(2):254–266
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
Doyel SA, Dugan JB, Patterson-Hine FA (1995) A combinatorial approach to modeling imperfect coverage. IEEE Trans Reliab 44(1):87–94
Dugan JB (1989) Fault trees and imperfect coverage. IEEE Transactions on Reliability 38(2):177–185
Dugan JB, Trivedi KS (1989) Coverage modeling for dependability analysis of fault-tolerant systems. IEEE Transactions on Computers 38(6):775–787
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
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
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
Kuo SY, Yeh FM, Lin HY (2007) Efficient and exact reliability evaluation for networks with imperfect vertices. IEEE Trans Reliab 56(2):288–300
Lee YJ, Na MG (2009) Design of delay-tolerant controller for remote control of nuclear reactor power. Nuclear Eng Technol 41(1):71–78
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
Levitin G (2005) Universal generating function in reliability analysis and optimization. Springer, London
Levitin G (2007) Block diagram method for analyzing multi-state systems with uncovered failures. Reliab Eng Syst Saf 92(6):727–734
Levitin G (2008) Optimal structure of multi-state systems with uncovered failures. IEEE Trans Reliab 57(1):140–148
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
Levitin G, Amari SV (2008b) Multi-state systems with multi-fault coverage. Reliab Eng Syst Saf 93(11):1730–1739
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
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
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
Myers AF (2007) k-out-of- n: G system reliability with imperfect fault coverage. IEEE Trans Reliab 56(3):464–473
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
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
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
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
Newton J (1995) Comment on: Reliability of k-out-of- n: G systems with imperfect fault-coverage. IEEE Trans Reliab 44(1):137–138
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
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
Pham H (1992a) Optimal cost-effective design of triple-modular-redundancy-with-spares systems. IEEE Transactions on Reliability 42(3):369–374
Pham H (1992b) Reliability analysis of a high voltage system with dependent failures and imperfect coverage. Reliab Eng Syst Saf 37(1):25–28
Pham H, Pham M (1992) Reliability analysis of dynamic redundant systems with imperfect coverage. Reliab Eng Syst Saf 35(2):173–176
Schneeweiss W (1987) Approximate fault-tree analysis with prescribed accuracy. IEEE Transactions on Reliability 36(2):250–254
Tian ZG, Zuo MJ, Huang HZ (2008) Reliability-redundancy allocation for multi-state series-parallel systems. IEEE Trans Reliab 57(2):303–310
Trivedi KS, Geist R (1983) Decomposition in reliability analysis of fault-tolerant systems. IEEE Trans Reliab 32(5):463–468
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
Ushakov I (1987) Optimal standby problems and a universal generating function. Soviet J Comput Syst Sci 25(4):79–82
Xing LD (2002) Analysis of generalized phased-mission system reliability, performance, and sensitivity. IEEE Trans Reliab 51(2):199–211
Xing LD (2007) Reliability evaluation of phased-mission systems with imperfect fault coverage and common-cause failures. IEEE Trans Reliab 56(1):58–68
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
Yeh FM, Lu SK, Kuo SY (2002) OBDD-Based evaluation of k-terminal network reliability. IEEE Trans Reliab 51(4):443–451
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
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
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag London
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-1-4471-4971-2_8
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4970-5
Online ISBN: 978-1-4471-4971-2
eBook Packages: EngineeringEngineering (R0)