The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.03 - July-September (2009 vol.6)
pp: 161-174
ABSTRACT
Multistate systems can model many practical systems in a wide range of real applications. A distinct characteristic of these systems is that the systems and their components may assume more than two levels of performance (or states), varying from perfect operation to complete failure. The nonbinary property of multistate systems and their components makes the analysis of multistate systems difficult. This paper proposes a new decision-diagram-based method, called multistate multivalued decision diagrams (MMDD), for the analysis of multistate systems with multistate components. Examples show how the MMDD models are generated and evaluated to obtain the system-state probabilities. The MMDD method is compared with the existing binary decision diagram (BDD)-based method. Empirical results show that the MMDD method can offer less computational complexity and simpler model evaluation algorithm than the BDD-based method.
INDEX TERMS
Binary decision diagram, multistate fault tree, multistate system, multistate multivalued decision diagram.
CITATION
Liudong Xing, Yuanshun Dai, "A New Decision-Diagram-Based Method for Efficient Analysis on Multistate Systems", IEEE Transactions on Dependable and Secure Computing, vol.6, no. 3, pp. 161-174, July-September 2009, doi:10.1109/TDSC.2007.70244
REFERENCES
[1] J. Huang and M. Zuo, “Dominant Multi-State Systems,” IEEETrans. Reliability, vol. 53, no. 3, pp. 362-368, Sept. 2004.
[2] Y.-R. Chang, S.V. Amari, and S.-Y. Kuo, “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.
[3] G. Levitin, “Reliability of Multi-State Systems with TwoFailure-Modes,” IEEE Trans. Reliability, vol. 52, no. 3, pp.340-348, Sept. 2003.
[4] G. Levitin, “Reliability Evaluation for Acyclic Transmission Networks of Multi-State Elements with Delays,” IEEE Trans. Reliability, vol. 52, no. 2, pp. 231-237, June 2003.
[5] G. Levitin, Y. Dai, M. Xie, and K.L. Poh, “Optimizing Survivability of Multi-State Systems with Multi-Level Protection by Multi-Processor Genetic Algorithm,” Reliability Eng. and System Safety, vol. 82, no. 1, pp. 93-104, Oct. 2003.
[6] 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.
[7] 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.
[8] J.B. Dugan and S.A. Doyle, “New Results in Fault-Tree Analysis,” Tutorial Notes of the Ann. Reliability and Maintainability Symp., Jan. 1996.
[9] M. Rausand and A. Hoyland, System Reliability Theory: Models, Statistical Methods, and Applications, second ed. Wiley-Interscience, 2003.
[10] A. Rauzy, “New Algorithms for Fault Tree Analysis,” Reliability Eng. and System Safety, vol. 40, pp. 203-211, 1993.
[11] L. Caldarola, “Coherent Systems with Multistate Components,” Nuclear Eng. and Design, vol. 58, pp. 127-139, 1980.
[12] M. Veeraraghavan and K.S. Trivedi, “Combinatorial Algorithm for Performance and Reliability Analysis Using Multistate Models,” IEEE Trans. Computers, vol. 43, no. 2, pp. 229-234, Feb. 1994.
[13] A.P. Wood, “Multistate Block Diagrams and Fault Trees,” IEEE Trans. Reliability, vol. 34, pp. 236-240, 1985.
[14] J. Xue and K. Yang, “Dynamic Reliability Analysis of Coherent Multistate Systems,” IEEE Trans. Reliability, vol. 44, no. 4, pp. 683-688, Dec. 1995.
[15] R.E. Barlow and A.S. Wu, “Coherent Systems with Multi-State Components,” Math. Operations Research, vol. 3, no. 4, pp. 275-281, 1978.
[16] E. El-Neweihi, F. Proschan, and J. Sethuraman, “Multistate Coherent Systems,” J. Applied Probability, vol. 15, pp. 675-688, 1978.
[17] W.S. Griffith, “Multistate Reliability Models,” J. Applied Probability, vol. 17, pp. 735-744, 1980.
[18] S.M. Ross, “Multivalued State Component Systems,” Annals of Probability, vol. 7, no. 2, pp. 379-383, 1979.
[19] C.Y. Lee, “Representation of Switching Circuits by Binary-Decision Programs,” Bell Systems Technical J., vol. 38, pp. 985-999, July 1959.
[20] R.T. Boute, “The Binary Decision Machine as a Programmable Controller,” EUROMICRO Newsletter, vol. 1, no. 2, pp. 16-22, Jan. 1976.
[21] S.B. Akers, “Binary Decision Diagrams,” IEEE Trans. Computers, vol. 27, no. 6, pp. 509-516, June 1978.
[22] R.E. Bryant, “Graph-Based Algorithms for Boolean Function Manipulation,” IEEE Trans. Computers, vol. 35, no. 8, pp. 677-691, Aug. 1986.
[23] D.M. Miller, “Multiple-Valued Logic Design Tools,” Proc. 23rdInt'l Symp. Multiple-Valued Logic (ISMVL), pp. 2-11, May 1993.
[24] D.M. Miller and R. Drechsler, “Implementing a Multiple-Valued Decision Diagram Package,” Proc. 28th Int'l Symp. Multiple-Valued Logic (ISVML), 1998.
[25] J.R. Burch, E.M. Clarke, D.E. Long, K.L. MacMillan, and D.L. Dill, “Symbolic Model Checking for Sequential Circuit Verification,” IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems, vol. 13, no. 4, pp. 401-424, 1994.
[26] G. Ciardo and R. Siminiceanu, “Saturation: An Efficient Iteration Strategy for Symbolic State Space Generation,” Tools and Algorithms for the Construction and Analysis of Systems, T. Margaria and W. Yi, eds., pp. 328-342, 2001.
[27] H. Hermanns, J. Meyer-Kayser, and M. Siegle, “Multi Terminal Binary Decision Diagrams to Represent and Analyse Continuous Time Markov Chains,” Numerical Solution of Markov Chains, W.J. Stewart, B. Plateau, and M. Silva, eds., pp. 188-207, 1999.
[28] A.S. Miner and S. Cheng, “Improving Efficiency of Implicit Markov Chain State Classification,” Proc. First Int'l Conf. Quantitative Evaluation of Systems (QEST '04), pp. 262-271, 2004.
[29] G. Ciardo, “Reachability Set Generation for Petri Nets: Can Brute Force Be Smart,” Proc. 25th Int'l Conf. Applications and Theory of Petri Nets (ICATPN '04), pp. 17-34, 2004.
[30] A.S. Miner and G. Ciardo, “Efficient Reachability Set Generation and Storage Using Decision Diagrams,” Application and Theory of Petri Nets, H. Kleijn and S. Donatelli, eds., pp. 6-25, 1999.
[31] D. Zampunieris, B.L. Charlier, “Efficient Handling of Large Sets ofTuples with Sharing Trees,” Proc. IEEE Data Compression Conf.(DCC '95), Oct. 1995.
[32] J.R. Burch, E.M. Clarke, K.L. McMillan, D.L. Dill, and L.J. Hwang, “Symbolic Model Checking: $10^{20}$ States and Beyond,” Proc.FifthAnn. IEEE Symp. Logic in Computer Science (LICS '90), pp. 1-33, 1990.
[33] M. Chechik, A. Gurfinkel, B. Devereux, A. Lai, and S. Easterbrook, “Data Structures for Symbolic Multi-Valued Model-Checking,” Formal Methods in System Design, vol. 29, no. 3, pp. 295-344, Nov. 2006.
[34] M.-M. Corsini and A. Rauzy, “Symbolic Model Checking andConstraint Logic Programming: A Cross-Fertilization,” Proc.Fifth European Symp. Programming (ESOP '94), pp. 180-194, Apr. 1994.
[35] O. Coudert and J.C. Madre, “Fault Tree Analysis: $10^{20}$ Prime Implicants and Beyond,” Proc. Ann. Reliability and Maintainability Symp., pp. 240-245, Jan. 1993.
[36] X. Zang, H. Sun, and K.S. Trivedi, “A BDD-Based Algorithm for Reliability Analysis of Phased-Mission Systems,” IEEE Trans. Reliability, vol. 48, no. 1, pp. 50-60, Mar. 1999.
[37] L. Xing, “Dependability Modeling and Analysis of Hierarchical Computer-Based Systems,” PhD dissertation, Dept. of Electrical and Computer Eng., Univ. of Virginia, May 2002.
[38] X. Zang, H. Sun, and K.S. Trivedi, “Dependability Analysis ofDistributed Computer Systems with Imperfect Coverage,” Proc.29th Ann. Int'l Symp. Fault-Tolerant Computing (FTCS '99), pp.330-337, 1999.
[39] L. Xing and J.B. Dugan, “Generalized Imperfect Coverage Phased-Mission Analysis,” Proc. Ann. Reliability and Maintainability Symp., pp. 112-119, Jan. 2002.
[40] 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.
[41] L. Xing and J.B. Dugan, “A Separable Ternary Decision Diagram Based Analysis of Generalized Phased-Mission Reliability,” IEEETrans. Reliability, vol. 53, no. 2, pp. 174-184, June 2004.
[42] M. Hsueh, T.K. Tsai, and R.K. Iyer, “Fault Injection Techniques and Tools,” Computer, vol. 30, no. 4, pp. 75-82, Apr. 1997.
[43] J.K. Vaurio, “Uncertainties and Quantification of Common CauseFailure Rates and Probabilities for System Analyses,” Reliability Eng. and System Safety, vol. 90, no. 2-3, pp. 186-195, Nov.-Dec. 2005.
[44] L. Xie, J. Zhou, and X. Wang, “Data Mapping and the Prediction ofCommon Cause Failure Probability,” IEEE Trans. Reliability, vol. 54, no. 2, pp. 291-296, June 2005.
[45] J.D. Andrews and S. Beeson, “Birnbaum's Measure of Component Importance for Noncoherent Systems,” IEEE Trans. Reliability, vol. 52, no. 2, pp. 213-219, June 2003.
[46] K.S. Brace, R.L. Rudell, and R.E. Bryant, “Efficient Implementation of a BDD Package,” Proc. 27th ACM/IEEE Design Automation Conf. (DAC '90), pp. 40-45, June 1990.
[47] T.H. Cormen, C.E. Leiserson, R.L. Rivest, and C. Stein, Introduction to Algorithms, second ed. MIT Press, 2001.
108 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool