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Issue No.10 - October (2010 vol.59)
pp: 1419-1433
Suprasad V. Amari , Parametric Technology Corporation, Greensburg
Liudong Xing , University of Massachusetts, Dartmouth
Akhilesh Shrestha , ARCON Corporation, Waltham
Jennifer Akers , Parametric Technology Corporation, Greensburg
Kishor S. Trivedi , Duke University, Durham
A distinct characteristic of multistate systems (MSS) is that the systems and/or their components may exhibit multiple performance levels (or states) varying from perfect operation to complete failure. MSS can model behaviors such as shared loads, performance degradation, imperfect fault coverage, standby redundancy, limited repair resources, and limited link capacities. The nonbinary state property of MSS and their components as well as dependencies existing among different states of the same component make the analysis of MSS difficult. This paper proposes efficient algorithms for analyzing MSS using multivalued decision diagrams (MDD). Various reliability, availability, and performability measures based on state probabilities or failure frequencies are considered. The application and advantages of the proposed algorithms are demonstrated through two examples. Furthermore, experimental results on a set of benchmark examples are presented to illustrate the advantages of the proposed MDD-based method for the performability analysis of MSS, as compared to the existing methods.
Benchmark, multistate system, multivalued decision diagrams, performability, reliability.
Suprasad V. Amari, Liudong Xing, Akhilesh Shrestha, Jennifer Akers, Kishor S. Trivedi, "Performability Analysis of Multistate Computing Systems Using Multivalued Decision Diagrams", IEEE Transactions on Computers, vol.59, no. 10, pp. 1419-1433, October 2010, doi:10.1109/TC.2009.184
[1] J. Huang and M. Zuo, "Dominant Multi-State Systems," IEEE Trans. Reliability, vol. 53, no. 3, pp. 362-368, Sept. 2004.
[2] L. Xing, "Efficient Analysis of Systems with Multiple States," Proc. IEEE 21st Int'l Conf. Advanced Information Networking and Applications, pp. 666-672, May 2007.
[3] S.V. Amari, J.B. Dugan, and R.B. Misra, "A Separable Method for Incorporating Imperfect Coverage in Combinatorial Model," IEEE Trans. Reliability, vol. 48, no. 3, pp. 267-274, Sept. 1999.
[4] L. Xing and J.B. Dugan, "A Separable Ternary Decision Diagrams Based Analysis of Generalized Phased-Mission Reliability," IEEE Trans. Reliability, vol. 53, no. 2, pp. 174-184, June 2004.
[5] L. Xing, "Reliability Evaluation of Phased-Mission Systems with Imperfect Fault Coverage and Common-Cause Failures," IEEE Trans. Reliability, vol. 56, no. 1, pp. 58-68, Mar. 2007.
[6] Z. Tang and J.B. Dugan, "BDD-Based Reliability Analysis of Phased-Mission Systems with Multimode Failures," IEEE Trans. Reliability, vol. 55, no. 2, pp. 350-360, June 2006.
[7] S. Kuo, Y. Chang, and S.V. Amari, "OBDD-Based Evaluation of Reliability and Importance Measures for Multistate Systems Subject to Imperfect Fault Coverage," IEEE Trans. Dependable and Secure Computing, vol. 2, no. 4, pp. 336-347, Oct.-Dec. 2005.
[8] A. Lisnianski and G. Levitin, Multi-State System Reliability. World Scientific, 2003.
[9] W. Li and H. Pham, "Reliability Modeling of Multi-State Degraded Systems with Multi-Competing Failures and Random Shocks," IEEE Trans. Reliability, vol. 54, no. 2, pp. 297-303, June 2005.
[10] X. Zang, D. Wang, H. Sun, and K.S. Trivedi, "A BDD-Based Algorithm for Analysis of Multistate Systems with Multistate Components," IEEE Trans. Computers, vol. 52, no. 12, pp. 1608-1618, Dec. 2003.
[11] L. Caldarola, "Coherent Systems with Multistate Components," Nuclear Eng. Design, vol. 58, pp. 127-139, 1980.
[12] M. Veeraraghavan and K.S. Trivedi, "A Combinatorial Algorithm for Performance and Reliability Analysis Using Multistate Models," IEEE Trans. Computers, vol. 43, no. 2, pp. 229-234, Feb. 1994.
[13] L. Xing and Y. Dai, "A New Decision Diagram Based Method for Efficient Analysis on Multi-State Systems," IEEE Trans. Dependable and Secure Computing, vol. 6, no. 3, pp. 161-174, July-Sept. 2009.
[14] A. Shrestha, L. Xing, and Y. Dai, "MBDD versus MMDD for Multistate Systems Analysis," Proc. Third IEEE Int'l Symp. Dependable, Autonomic and Secure Computing, pp. 172-180, Sept. 2007.
[15] R. Bryant, "Graph Based Algorithms for Boolean Function Manipulation," IEEE Trans. Computers, vol. 35, no. 8, pp. 677-691, Aug. 1986.
[16] A. Srinivasan, T. Kam, S. Malik, and R.K. Brayton, "Algorithms for Discrete Function Manipulation," Proc. IEEE Int'l Conf. Computer-Aided Design, pp. 92-95, Nov. 1990.
[17] D.M. Miller and R. Drechsler, "Implementing a Multiple-Valued Decision Diagram Package," Proc. 28th Int'l Symp. Multiple-Valued Logic, 1998.
[18] L. Xing and J.B. Dugan, "Dependability Analysis Using Multiple-Valued Decision Diagrams," Proc. Sixth Int'l Conf. Probabilistic Safety Assessment and Management, June 2002.
[19] M. Rausand and A. Høyland, System Reliability Theory: Models, Statistical Methods, and Applications. Wiley-Interscience, 2003.
[20] T. Kam, T. Villa, R. Brayton, and A. Sangiovanni-Vincentelli, Synthesis of Finite State Machines: Functional Optimization. Kluwer Academic Publishers, Nov. 1996.
[21] T. Kam, T. Villa, R. Brayton, and A. Sangiovanni-Vincentelli, "Multi-Valued Decision Diagrams for Logic Synthesis and Verification," Multi-Valued Logic—An Int'l J., special issue: decision diagrams, vol. 4, nos. 1/2, pp. 9-62, 1998.
[22] I. Wegener, Branching Programs and Binary Decision Diagrams: Theory and Applications, Monographs on Discrete Mathematics and Applications. Soc. for Industrial Math., 2000.
[23] R. Drechsler and D. Sieling, "Binary Decision Diagrams in Theory and Practice," Int'l J. Software Tools for Technology Transfer, vol. 3, no. 2, pp. 112-136, 2001.
[24] T.H. Cormen, C.E. Leiserson, R.L. Rivest, and C. Stein, Introduction to Algorithms, second ed. MIT Press, 2001.
[25] MCNC Benchmarks, benchmarks/ LGSynth91LGSynth91.tar.Z, 2007.
[26] MCNC Benchmarks, benchmarks/ LGSynth91twolexamples/, 2007.
[27] S. Yang, "Logic Synthesis and Optimization Benchmarks User Guide Version 3.0," technical report, Microelectronics Center of North Carolina, , Jan. 1991.
[28] L. Xing and J.B. Dugan, "Analysis of Generalized Phased Mission System Reliability, Performance and Sensitivity," IEEE Trans. Reliability, vol. 51, no. 2, pp. 199-211, June 2002.
[29] D. Wang and K.S. Trivedi, "Computing Steady-State Mean Time to Failure for Non-Coherent Repairable Systems," IEEE Trans. Reliability, vol. 54, no. 3, pp. 506-516, Sept. 2005.
[30] K.S. Trivedi, J.K. Muppala, S.P. Woolet, and B.R. Haverkort, "Composite Performance and Dependability Analysis," Performance Evaluation, vol. 14, pp. 197-215, Feb. 1992.
[31] R.A. Sahner, K.S. Trivedi, and A. Puliafito, Performance and Reliability Analysis of Computer Systems: An Example-Based Approach Using the SHARPE Software Package. Kluwer Academic Publishers, 1995.
[32] B. Haverkort, R. Marie, G. Rubino, and K.S. Trivedi, Performability Modeling Tools and Techniques. John Wiley and Sons, 2001.
[33] J. Xue and K. Yang, "Dynamic Reliability Analysis of Coherent Multistate Systems," IEEE Trans. Reliability, vol. 44, no. 4, pp. 683-688, Dec. 1995.
[34] Y.W. Liu and K.C. Kapur, "Reliability Measures for Dynamic Multistate Nonrepairable Systems and Their Applications to System Performance Evaluation," IIE Trans., vol. 38, pp. 511-520, 2000.
[35] S.V. Amari and R.B. Misra, "Comment on: Dynamic Reliability Analysis of Coherent Multistate Systems," IEEE Trans. Reliability, vol. 46, no. 4, pp. 460-461, Dec. 1997.
[36] S.V. Amari, "Generic Rules to Evaluate System Failure-Frequency," IEEE Trans. Reliability, vol. 49, no. 1, pp. 85-87, Mar. 2000.
[37] Y.R. Chang, S.V. Amari, and S. Kuo, "Computing System Failure Frequencies and Reliability Importance Measures Using OBDD," IEEE Trans. Computers, vol. 53, no. 1, pp. 54-68, Jan. 2004.
[38] J.D. Murchland, "Fundamental Concepts and Relations for Reliability Analysis of Multistate Systems," Reliability and Fault Tree Analysis, R.E. Barlow, J.B. Fussell, and N.D. Singpunvalla, eds., pp. 581-618, SIAM, 1975.
[39] E. Korczak, "Rules for Failure/Repair Frequency Evaluation of Multi-State Systems," Proc. European Safety and Reliability Conf. 2006 (ESREL '06), vol. 1, pp. 157-164, Sept. 2006.
[40] E. Korczak, "New Formula for the Failure/Repair Frequency of Multi-State Monotone Systems and Its Applications," Control and Cybernetics, vol. 36, no. 1, pp. 219-239, 2007.
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