International Journal of Engineering and Manufacturing(IJEM)

ISSN: 2305-3631 (Print), ISSN: 2306-5982 (Online)

Published By: MECS Press

IJEM Vol.2, No.2, Apr. 2012

Calculation of Failure Probability of Series and Parallel Systems for Imprecise Probability

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Bin Suo, Yong-sheng Cheng, Chao Zeng , Jun Li

Index Terms

Reliability, failure probability, series-parallel systems, D-S evidence theory


In the situation that unit failure probability is imprecise when calculation the failure probability of system, classical probability method is not applicable, and the analysis result of interval method is coarse. To calculate the reliability of series and parallel systems in above situation, D-S evidence theory was used to represent the unit failure probability. Multi-sources information was fused, and belief and plausibility function were used to calculate the reliability of series and parallel systems by evidential reasoning. By this mean, lower and upper bounds of probability distribution of system failure probability were obtained. Simulation result shows that the proposed method is preferable to deal with the imprecise probability in reliability calculation, and can get additional information when compare with interval analysis method.

Cite This Paper

Bin Suo, Yong-sheng Cheng, Chao Zeng , Jun Li,"Calculation of Failure Probability of Series and Parallel Systems for Imprecise Probability", IJEM, vol.2, no.2, pp.79-85, 2012.


[1] Ben-Haim Y, “Convex models of uncertainty in radial pulse buckling of shells,” Journal of Applied Mechanics, vol. 60, no. 3, pp. 683-688, March 1993.

[2] Elishakof I, “Essay on uncertainties in elastic and viscoelastic structures: From A.M. Freudenthal's criticisms to modem convex modeling,” Computers and Structures, vol. 56, n. 6, pp. 871-895, June 1995.

[3] Ben-Haim Y, “An non-probabilistic concept of reliability,” Structural Safety, vol. 14, n. 4, pp. 227-245, April 1994.

[4] Yakov Ben-Haim, “Uncertainty, probability and information-gaps,” Reliability Engineering and System Safety, vol. 85, n. 2, pp. 249-266, February 2004.

[5] S. Gareth Pierce, Yakov Ben-Haim, et al. , “Evaluation of Neural Network Robust Reliability Using Information-Gap Theory,” IEEE Transactions on Neural Networks, vol. 17, n. 6, pp. 1349-1361, June 2006.

[6] Scott J. Duncan, Bert Bras, Christiaan J.J. Paredis, “An approach to robust decision making under severe uncertainty in life cycle design,” International Journal of Sustainable Design, vol. 1, n. 1, pp. 45-59, January 2008.

[7] Qiu Zhiping, Chen Suhuan, Elishakof I, “Non-probabilistic eigenvalue problem for structures with uncertain parameters via interval analysis,” Chaos, Solitons and Fractals, vol. 7, n. 3, pp. 303-308, March 1996.

[8] Weidong Wu, S.S. Rao, “Uncertainty analysis and allocation of joint tolerances in robot manipulators based on interval analysis,” Reliability Engineering and System Safety, vol. 92, n. 1, pp. 54-64, January 2007.

[9] C. Jiang X. Han, F. J. Guan, Y. H. Li, “An uncertain structural optimization method based on nonlinear interval number programming and interval analysis method,” Engineering Structures, vol. 29, n. 11, November 2007. 

[10] Fahed Abdallah, Amadou Gning, Philippe Bonnifait, “Box particle filtering for nonlinear state estimation using interval analysis,” Automatica, vol. 44, n. 3, March 2008.

[11] D. Harmance, G. J. Klir, “Measuring total uncertainty in Dempster-Shafer theory: A novel approach,” International Journal of General Systems, vol. 22, n. 4, pp. 405-419, April 1997.

[12] R. R. Yager, “Arithmetic and other operations on Dempster-Shafer structures,” International Journal of Man-machine Studies, vol. 25, pp. 357-366, June 1986.

[13] Dempster A P, “Upper and lower probabilities induced by a multi valued mapping,” Annals Math Statist, vol. 38, no. 2, pp. 325-339, 1967.

[14] Shafer G. A, Mathematical Theory of Evidence. Princeton University Press, 1976.

[15] C. Joslyn, J.C. Helton, “Bounds on belief and plausibility of functionality propagated random sets,” 2002 Annual Meetings of the North American Fuzzy Information Processing Society, pp.27-29, June 2002, New Orleans, LA, IEEE, Piscataway, NJ, pp:412-417, 2002.

[16] Harish Agarwal, John E. Renaud, Evan L, “Preston, et al. Uncertainty quantification using evidence theory in multidisciplinary design optimization,” Reliability Engineering and System Safety, vol. 85, n. 1, pp. 281-294, January 2004.