Abstract
Fault tolerance has been an essential architectural attribute for achieving high reliability in many critical applications of digital systems. Automatic fault detection, location, isolation, recovery, and reconfiguration mechanisms play a crucial role in implementing fault tolerance because a not-covered fault may lead to a system or subsystem failure even when adequate redundancy exists. The probability of successfully recovering from a fault given that the fault has occurred is known as the coverage factor or coverage and this is used to account for the efficiency of fault-tolerant mechanisms. If the fault and error handling mechanisms cannot successfully cover all faults in the system, then the coverage factor becomes less than unity and the system is said to have imperfect coverage. The models that consider the effects of imperfect fault coverage are known as imperfect fault coverage models or simply imperfect coverage models, fault coverage models, or coverage models. For systems with imperfect fault coverage, an excessive level of redundancy may even reduce the system reliability. Therefore, an accurate analysis must account for not only the system structure but also the system fault and error handling behavior, which is often called coverage behavior. The appropriate coverage modeling approach depends on the type of fault tolerant techniques used. In this chapter, we present the status and trends of imperfect coverage models, and associated reliability analysis techniques. We also present the historical developments, modeling approaches, reliability algorithms, optimal design policies, and available software tools.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Amari SV. Reliability, risk and fault-tolerance of complex systems. PhD Dissertation, Indian Institute of Technology, Kharagpur, 1997.
Amari SV, Pham H, Dill G. Optimal design of k-out-of-n:G subsystems subjected to imperfect fault-coverage. IEEE Trans. on Reliability 2004; 53:567–575.
Amari SV, McLaughlin L, Yadlapati B. Optimal cost-effective design of parallel systems subject to imperfect fault-coverage. Proc. IEEE Ann. Reliability and Maintainability Symp., Tampa, Florida Jan. 2003; 29–34.
Amari SV, Dugan JB, Misra RB. Optimal reliability of systems subject to imperfect faultcoverage. IEEE Trans. on Reliability 1999; 48:275–284.
Amari SV, Dugan JB, Misra RB. A separable method for incorporating imperfect fault-coverage into combinatorial models. IEEE Trans. on Reliability 1999; 48: 267–274.
Amari SV, Myers A, Rauzy A. An efficient algorithm to analyze new imperfect fault coverage models. Proc. Ann. Reliability and Maintainability Symp. Orlando, FL. Jan. 2007;420–426.
Arnold TF. The concept of coverage and its effect on the reliability model of a repairable system. IEEE Trans. on Computers 1973; C-22:325–339.
Avizienis A, Laprie JC, Randell B, Landwehr C. Basic concepts and taxonomy of dependable and secure computing. IEEE Trans. on Dependable and Secure Computing 200; 1:11–33.
Bavuso SJ et. al., HiRel: Hybrid automated reliability predictor tool system (Version 7.0), NASA TP 3452, 1994.
Bavuso SJ, Dugan JB, Trivedi KS, Rothmann EM, Smith WE. Analysis of typical fault-tolerant architectures using HARP. IEEE Trans. on Reliability 1987; R-36:176–185.
Bobbio A. Trivedi KS. An aggregation technique for the transient analysis of stiff Markov chains. IEEE Trans. on Computers 1986; 35:803–814.
Bouricius WG, Carter WC, Schneider PR. Reliability modeling techniques for self-repairing computer systems. 24th Ann. ACM National Conf. 1969; 295–309.
Bouricius WG, Carter WC, Jessep DC, Schneider PR, Wadia AB. Reliability modeling for fault-tolerant computers. IEEE Trans. on Computers 1971; C-20:1306–1311.
Boyd MA, Veeraraghavan M, Dugan JB, Trivedi KS. An approach to solving large reliability models. Proc. of IEEE/AIAA 8th Embedded Digital Avionics Conf. 1988; 243–250.
Butler RW, Hayhurst KJ, Johnson SC. A note about HARP’s state trimming method. NASA/TM-1998-208427, 1998.
Chang YR, Amari SV, Kuo S. Computing system failure frequencies and reliability importance measures using OBDD. IEEE Trans. on Computers 2003; 53: 54–68.
Chang YS, Amari V, Kuo SY. Reliability evaluation of multi-state systems subject to imperfect coverage using OBDD. Proc. Pacific Rim Int. Symp. Dependable Computing (PRDC), Tsukuba, Japan, Dec. 16–18, 2002;193–200.
Chang YR, Amari SV, Kuo SY. OBDD-based evaluation of reliability and importance measures for multistate systems subject to imperfect fault coverage. IEEE Trans. on Dependable and Secure Computing 2005; 2:336–347.
Conn RB, Merryman PM, Whitelaw KL. CAST—A complementary analytic-simulative technique for modeling fault-tolerant computing systems. Proc. AIAA Computer Aero. Conf. 1977; 6.1–6.27.
Cukier M, Powell D, Arlat J. Coverage estimation methods for stratified fault-injection. IEEE Trans. on Computers 1999; 48:707–723.
Doyle SA, Dugan JB, Boyd M. Combinatorial-models and coverage: a binary decision diagram (BDD) approach. Proc. Ann. Reliability and Maintainability Symp., Washington D.C., Jan. 16–19, 1995; 82–89.
Doyle SA, Dugan JB, Patterson-Hine FA. A combinatorial approach to modeling imperfect coverage. IEEE Trans. on Reliability 1995; 44:87–94.
Dugan JB, Trivedi KS. Coverage modeling for dependability analysis of fault-tolerant systems. IEEE Trans. on Computers 1989; 38:775–787.
Dugan JB. Fault trees and imperfect coverage. IEEE Trans. on Reliability 1989; 38:177–185.
Dugan JB. Fault-tree analysis of computer-based systems. Tutorial Notes, RAMS, Reliability and Maintainability Symp., Los Angeles, CA, Jan. 26–29, 2004.
Dutuit Y, Rauzy A. New insights in the assessment of k-out-of-n and related systems. Reliability Engineering and System Safety 2001; 72:303–314.
Geist R, Trivedi KS. Reliability estimation of fault-tolerant systems: Tools and techniques. IEEE Computer, Special Issue on Fault-tolerant Computing 1990; 23: 52–61.
Geist R. Extended behavioral decomposition for estimating ultrahigh reliability. IEEE Trans. on Reliability 1991; 40:22–28.
Geist R, Smotherman M, Trivedi KS, Dugan JB. The reliability of life-critical computer systems., Acta Informatica 1986; 23:621–642.
Ibe OC, Howe RC, Trivedi KS. Approximate availability analysis of VAXcluster systems. IEEE Trans. on Reliability 1989; 38:146–152.
Johnson AM Jr., Malek M. Survey of software tools for evaluating reliability, availability, and serviceability. ACM Computing Surveys 1988; 20:227–269.
Kuo W, Zuo MJ. Optimal reliability modeling. Wiley, New York, 2003.
Levitin G. Block diagram method for analyzing multi-state systems with uncovered failures. Reliability Engineering and System Safety 2007; 92:727–734.
Levitin G. Optimal structure of multi-state systems with uncovered failures. IEEE Trans. on Reliability, March 2007; 57(1): 140–148.
Levitin G, Amari SV. Reliability analysis of fault tolerant systems with multi-fault coverage. International Journal of Performability Engineering, 2007; 3(4): 441–451.
Levitin G, Amari SV. Multi-state Systems with multi-fault coverage. Reliability Engineering and System Safety, in press, 2008.
Levitin G, Amari SV. Multi-state Systems with static performance dependent coverage. Proc. Institution of Mechanical Engineers, Part O, Journal of Risk and Reliability, accepted for publication,to appear in 2008.
Lindemann C, Malhotra M, Trivedi KS. Numerical methods for reliability evaluation of Markov closed fault-tolerant systems. IEEE Trans. on Reliability 1995; 44:694–704.
Malhotra M, Muppula J, Trivedi KS. Stiffnesstolerant methods for transient analysis of stiff Markov chains. Microelectronics and Reliability 1994; 34:1825–1841.
Malhotra M, Trivedi KS. Data integrity analysis of disk array systems with analytic modeling of coverage. Performance Evaluation 1995; 22:111–133.
Mathur FP, Avizienis A. Reliability analysis and architecture of a hybrid-redundant digital system: Generalized triple modular redundancy with repair. Proc. AFIPS SJCC 1970; 36:375–383.
McGough J, Smotherman M, Trivedi KS. The conservativeness of reliability estimates based on instantaneous coverage. IEEE Trans. on Computers 1985; 34: 602–609.
Misra KB. Reliability analysis and prediction: A methodology oriented treatment. Elsevier, Amsterdam, 1992.
Myers AF. k-out-of-n:G system reliability with imperfect fault coverage. IEEE Trans. on Reliability, Sept. 2007; 56(3): 464–473.
Myers AF, Rauzy A. Assessment of redundant systems with imperfect coverage by means of binary decision diagrams. Reliability Engineering and System Safety. July 2008; 93(7): 1025–1035.
Myers AF, Rauzy A. Efficient reliability assessment of redundant systems subject to imperfect fault coverage using binary decision diagrams. Accepted to appear in IEEE Trans. on Reliability, DOI: 10.1109/TR 2008. 916884.
Najjar WA, Gaudiot J. Scalability analysis in gracefully-degradable large systems. IEEE Trans. on Reliability 1991; 40: 89–197.
Ng YW, Avizienis A. ARIES: An automated reliability estimation system. Proc. Ann. Reliability and Maintainability Symp. Philadelphia, PA; Jan. 18–20, 1977; 108–113.
Pham H. Optimal cost-effective design of triple modular redundancy with spares systems. IEEE Trans. on Reliability 1993; 42:369–374.
Rangarajan S, Huang Y, Tripathi SK. Computing reliability intervals for k-resilient protocols. IEEE Trans. on Computers 1995; 44:462–466.
Rauzy A. new algorithms for fault tree analysis. Reliability Engineering and System Safety 1993; 40:203–211.
Rauzy A. Aralia user’s manual. ARBoost Technologies 2006.
Sahner RA, Trivedi KS. Puliafito A. Performance and reliability analysis of computer systems. Kluwer, Dordrecht, 1996.
Shooman ML. Reliability of computer systems and networks: Fault tolerance, analysis, and design. Wiley, New York, 2002.
Smotherman M, Geist RM, Trivedi KS. Provably conservative approximations to complex reliability models. IEEE Trans. on Computers 1986; C-35: 333–338.
Trivedi KS, Geist RM. A tutorial on the CARE III approach to reliability modeling. NASA Contractor Report, 1981; 3488.
Trivedi KS. Probability and statistics with reliability, queuing, and computer science applications. Wile, New York, 2001.
Trivedi KS, Geist R. Decomposition in reliability analysis of fault tolerant systems. IEEE Trans. on Reliability 1983; R-32:463–468.
Trivedi KS, Dugan JB, Geist R, Smotherman M. Modeling imperfect coverage in fault-tolerant systems. Fault-Tolerant Computing Symp. (FTCS) IEEE Computer Society, 1984; 77–82.
Trivedi KS, Sathaye AS, Ibe OC, Howe RC. Should I add a processor? 23rd Annual Hawaii International Conference on System Sciences. IEEE Computer Society Press; Jan. 1990:214–221.
Trivedi KS, Dugan JB, Geist R, Smotherman M. Hybrid reliability modeling of fault-tolerant computer systems. Computers and Electrical Engineering, 1984; 11:87–108.
Vaurio JK. Treatment of general dependencies in system fault-tree and risk analysis. IEEE Trans. on Reliability 2002; 51:278–287.
Vesely W. et al. Fault tree handbook with aerospace applications, Version 1.1, NASA Publication, Aug. 2002.
Xing L, Dugan JB. Analysis of generalized phased-mission systems reliability, performance, and sensitivity. IEEE Trans. on Reliability 2002; 199–211.
Xing L, Dugan JB. Dependability analysis using multiple-valued decision diagrams. 6th Int’l. Conf. Problems in Safety Assessment and Management (PSAM6) 2002.
Xing L, Dugan JB. Dependability analysis of hierarchical systems with modular imperfect coverage. Proc. 19th Int. System Safety Conf. (ISSC) 2001; 347–356.
Xing L. Reliability importance analysis of generalized phased-mission systems. International Journal of Performability Engineering 2007; 3:303–318.
Xing L, Dugan JB. A separable ternary decision diagram based analysis of generalized phased-mission reliability. IEEE Trans. on Reliability 2004; 53: 174–184.
Zang X, Sun H, Trivedi KS. Dependability analysis of distributed computer systems with imperfect coverage. Proc. 29th Ann. Int. Symp. Fault-Tolerant Computing (FTCS-29); IEEE Computer Society, IEEE Press, Madison, WI, 1999: 330–337.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag London Limited
About this chapter
Cite this chapter
Amari, S.V., Myers, A.F., Rauzy, A., Trivedi, K.S. (2008). Imperfect Coverage Models: Status and Trends. In: Misra, K.B. (eds) Handbook of Performability Engineering. Springer, London. https://doi.org/10.1007/978-1-84800-131-2_22
Download citation
DOI: https://doi.org/10.1007/978-1-84800-131-2_22
Publisher Name: Springer, London
Print ISBN: 978-1-84800-130-5
Online ISBN: 978-1-84800-131-2
eBook Packages: EngineeringEngineering (R0)