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Reliability Analysis of 6-Component Lattice Load-sharing Markov Repairable System with Spatial Dependence

Volume 13, Number 3, May 2017 - Paper 4 - pp. 279-287

Liying Wang, Yuran Tian, and Zhaona Pei

Shijiazhuang Tiedao Institute, Shijiazhuang, 050043 CHINA

(Submitted on November 13, 2016; Revised on April 17, 2017; Accepted on April 24, 2017)


This paper proposes a new model that generalizes the traditional Markov repairable system to the case of spatial dependence among components. The components of the system are identical and arranged in two lines and consist of a lattice. The performance of each component depends on its spatial “neighbours” and the number of failed components in other lines. Markov process is adopted to model the performance of the system. The state space and transition rate matrix corresponding to a 6-component lattice load-sharing system with spatial dependence are presented. Availability of the system is obtained via Markov theory and Laplace transform method. A numerical example is given to illustrate the results in this paper. The states of the system are partitioned into four state sets: security, degraded, warning, and failed. The probabilities of visiting to four state sets are also discussed in the numerical example. The work might provide a basis for the reliability analysis of load-sharing systems with interacting components that themselves be arranged in some two-dimensional spatial pattern.


References: 16

1. W. Kuo and M.J. Zuo, “Optimal reliability modelling”, Wiley, New York, 2003.
2. K.C. Kapur and L.R. Lamberson, “Reliability in engineering design”, Wiley, New York, 1977.
3. R.K. Iyer and D.P. Rossetti, “A measurement-based model for workload dependency of CPU errors”, IEEE Transactions on Computer; vol.35, no.6, pp. 511-519, 1986.
4. A. Barros, C. Berenguer and A. Grall, “Optimization of replacement times using imperfect monitoring information”, IEEE Transactions on Reliability, vol.52, no.4, pp. 523–533, 2003.
5. S.V. Amari, K.B, Krishna, H. Pham, “Tampered failure fate load-sharing systems: status and perspectives”. Handbook of Performability Engineering, pp. 291-308, 2008.
6. M. Jain, R. Gupta, “Load sharing M-out of-N: G system with non-identical components subject to common cause failure”, Int. J. Mathematics in Operational Research,  vol.4, no.5, pp. 586-605, 2012.
7. L.Y. Wang, X.J. Jia and J. Zhang, “Reliability evaluation for Multi-State Markov repairable systems with redundant dependencies”, Quality Technology and Quantitative Management, vol.10, no.3, pp. 277-289, 2013.
8. H.Y. Yu, C.B. Chu, E. Chatelet and F Yalaoui, “Reliability optimization of a redundant system with failure dependencies”, Reliability Engineering and System Safety, vol.92, no.12, pp. 1627-1634, 2007.
9. G. Levitin and L.D. Xing, “Reliability and performance of multi-state systems with propagated failures having selective effect”, Reliability Engineering and System Safety, vol. 95, no. 6, pp. 655–661, 2010.
10. G. Maaroufi, A. Chelbi and N. Rezg, “Optimal selective renewal policy for systems subject to propagated failures with global effect and failure isolation phenomena”, Reliability Engineering and System Safety, vol. 114, no. 6, pp. 61-70, 2013.
11. L.Y. Wang and S.B. Si, “Reliability analysis of circular Markov repairable systems with spatial dependence”, Journal of northwestern polytechnical university, vol. 32, no. 6, pp. 923-928, 2014.
12. F. Ball, R.K. Milne and G.F. Yeo, “Multivariable semi-Markov analysis of burst properties of multi-conductance single ion channels”, Journal of Applied Probability, vol. 39, no. 1, pp. 179-196, 2002.
13. A. Lisnianski and G. Levitin, “Multi-state system reliability, assessment, optimization and application”, Singapore: World Scientific Publishing Co. Pte. Ltd., 2003.
14. D.V. Widder, “The Laplace Transform”, Princeton University Press, 1946.
15. N. Saqib, and M.T. Siddiqi, “Aggregation of safety performance indicators to higher-level indicators”, Reliability Engineering and System Safety, vol. 93, no. 2, pp. 307-315, 2008.
16. L.Y. Wang and L.R. Cui, “Performance evaluation of aggregated Markov repairable systems with multi-operating levels”, Asia-Pacific Journal of Operational Research, vol. 30, no. 4, pp. 1350003-1-27, 2013.


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