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Joint interval reliability for Markov systems with an application in transmission line reliability

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  • Csenki, Attila

Abstract

We consider Markov reliability models whose finite state space is partitioned into the set of up states U and the set of down states D. Given a collection of k disjoint time intervals Iℓ=[tℓ,tℓ+xℓ], ℓ=1,…,k, the joint interval reliability is defined as the probability of the system being in U for all time instances in I1∪⋯∪Ik. A closed form expression is derived here for the joint interval reliability for this class of models. The result is applied to power transmission lines in a two-state fluctuating environment. We use the Linux versions of the free packages Maxima and Scilab in our implementation for symbolic and numerical work, respectively.

Suggested Citation

  • Csenki, Attila, 2007. "Joint interval reliability for Markov systems with an application in transmission line reliability," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 685-696.
    • Handle: RePEc:eee:reensy:v:92:y:2007:i:6:p:685-696
    DOI: 10.1016/j.ress.2006.11.007
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    References listed on IDEAS

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    1. A. Csenki, 1994. "Joint availability of systems modelled by finite semi–markov processes," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 10(4), pages 279-293.
    2. Mico Mrkaic, 2001. "Scilab as an econometric programming system," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(4), pages 553-559.
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    Cited by:

    1. Shijia Du & Lirong Cui & Cong Lin, 2016. "Some reliability indexes and sojourn time distributions for a repairable degradation model," Journal of Risk and Reliability, , vol. 230(3), pages 334-349, June.
    2. Du, Shijia & Zeng, Zhiguo & Cui, Lirong & Kang, Rui, 2017. "Reliability analysis of Markov history-dependent repairable systems with neglected failures," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 134-142.
    3. Gao, Hongda & Cui, Lirong & Yi, He, 2019. "Availability analysis of k-out-of-n: F repairable balanced systems with m sectors," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    4. Csenki, Attila, 2011. "On continuous lifetime distributions with polynomial failure rate with an application in reliability," Reliability Engineering and System Safety, Elsevier, vol. 96(11), pages 1587-1590.
    5. Yi, He & Cui, Lirong & Shen, Jingyuan & Li, Yan, 2018. "Stochastic properties and reliability measures of discrete-time semi-Markovian systems," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 162-173.
    6. Liu, Baoliang & Cui, Lirong & Wen, Yanqing & Shen, Jingyuan, 2013. "A performance measure for Markov system with stochastic supply patterns and stochastic demand patterns," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 294-299.
    7. Cui, Lirong & Chen, Jianhui & Wu, Bei, 2017. "New interval availability indexes for Markov repairable systems," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 12-17.
    8. A Csenki, 2007. "On the three-state weather model of transmission line failures," Journal of Risk and Reliability, , vol. 221(3), pages 217-228, September.
    9. Baoliang Liu & Lirong Cui & Yanqing Wen, 2014. "Interval reliability for aggregated Markov repairable system with repair time omission," Annals of Operations Research, Springer, vol. 212(1), pages 169-183, January.
    10. Csenki, Attila, 2009. "Stochastic demand patterns for Markov service facilities with neutral and active periods," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 382-393.
    11. Dhople, S.V. & DeVille, L. & Domínguez-García, A.D., 2014. "A Stochastic Hybrid Systems framework for analysis of Markov reward models," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 158-170.
    12. Yi, He & Cui, Lirong & Balakrishnan, Narayanaswamy, 2021. "New reliability indices for first- and second-order discrete-time aggregated semi-Markov systems with an application to TT&C system," Reliability Engineering and System Safety, Elsevier, vol. 215(C).

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