Reliability Evaluation of Two-Stage Directed Semi-Markov Repairable Network Systems

Abstract

A two-stage directed Semi-Markov repairable network system is presented in this paper to model the performance of many transmission systems, such as power or oil transmission network, water or gas supply network, etc. The availability of the system is discussed by using Markov renewal theory, Laplace transform and probability analysis methods. A numerical example is given to illustrate the results obtained in the paper.

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R. Fan, L. Wang and T. Li, "Reliability Evaluation of Two-Stage Directed Semi-Markov Repairable Network Systems," Applied Mathematics, Vol. 4 No. 4, 2013, pp. 690-693. doi: 10.4236/am.2013.44095.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] A. Lisnianski and G. Levitin, “Multi-State System Reliability, Assessment, Optimization and Application,” World Scientific Publishing Co. Pte. Ltd., Singapore City, 2003.
[2] K. S. Prabhata and K. S. Ashok, “Design of Water Supply Pipe Networks,” John Wiley & Sons, Inc., Hoboken, 2008.
[3] L. Wang, L. Cui and H. Sun, “Reliability Evaluation of Multi-State Two-Stage Directed Network Systems by Using Universal Generating Function,” Journal of Beijing Institute of Technology, Vol. 19, Suppl. 1, 2010, pp. 83-85.
[4] H. Sun and L. Wang, “Reliability Evaluation of Multi State Two-Stage Directed Network Systems by Using Combined Stochastic Process Methods and Universal Generating Function,” 2nd International Workshop on Datebase Technology and Applications, Wuhan, 27-28 November 2010, pp. 411-414.
[5] I. Ushakov, “Universal Generating Function,” Soviet Journal of Computer and Systems Sciences, Vol. 24, No. 5, 1986, pp. 118-129.
[6] G. Levitin, “Universal Generating Function and Its Applications,” Springer, Berlin, 2005.
[7] A. Lisnianski and Y. Ding, “Redundancy Analysis for Repairable Multi-State System by Using Combined Stochastic Process Methods and Universal Generating Function Technique,” Reliability Engineering and System Safety, Vol. 94, No. 11, 2009, pp. 1788-1795. doi:10.1016/j.ress.2009.05.006
[8] M. Yu and L. Cui, “Modeling and Analysis for Two Stage Directed Network Markov Repairable Systems,” Transactions of Beijing Institute of Technology, Vol. 31, No. 6, 2011, pp. 753-756.
[9] M. Yu and L. Cui, “A Study on Optimal Availability for A Two-Stage Directed Network of Markov Repairable Systems,” The 4th Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modeling, Wellington, 2010, pp. 796-803.
[10] E. Cinlar, “Markov Renewal Theory: A Survey,” Management Science, Vol. 21, No. 7, 1975, pp. 727-752. doi:10.1287/mnsc.21.7.727

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