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Some reliability indexes and sojourn time distributions for a repairable degradation model

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  • Shijia Du
  • Lirong Cui
  • Cong Lin

Abstract

In this article, a degradation model for repairable systems is developed, based on a continuous-time Markov process with multiple discrete states. The discrete states are divided into two types: up and down states, and represent that the system is undergoing a range of degradation levels from perfect functioning to complete failure. The closed-form expressions of four common reliability indexes are derived using the technique of aggregated stochastic process. The indexes include point availability, multi-point availability, interval availability and multi-interval availability. Also, the analytical solution to lower degradation probabilities and some sojourn time distributions are derived using the technique of aggregated stochastic process. Finally, numerical examples are given to illustrate the results obtained in the article.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:risrel:v:230:y:2016:i:3:p:334-349
    DOI: 10.1177/1748006X16633036
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    References listed on IDEAS

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    1. Lirong Cui & Shijia Du & Aofu Zhang, 2014. "Reliability measures for two-part partition of states for aggregated Markov repairable systems," Annals of Operations Research, Springer, vol. 212(1), pages 93-114, January.
    2. Moghaddass, Ramin & Zuo, Ming J., 2012. "A parameter estimation method for a condition-monitored device under multi-state deterioration," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 94-103.
    3. Alan Hawkes & Lirong Cui & Zhihua Zheng, 2011. "Modeling the evolution of system reliability performance under alternative environments," IISE Transactions, Taylor & Francis Journals, vol. 43(11), pages 761-772.
    4. Lirong Cui & Shijia Du & Alan Hawkes, 2012. "A study on a single-unit repairable system with state aggregations," IISE Transactions, Taylor & Francis Journals, vol. 44(11), pages 1022-1032.
    5. 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.
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    Cited by:

    1. Wu, Bei & Cui, Lirong & Fang, Chen, 2019. "Reliability analysis of semi-Markov systems with restriction on transition times," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.
    2. Å nipas, Mindaugas & Radziukynas, Virginijus & ValakeviÄ ius, Eimutis, 2018. "Numerical solution of reliability models described by stochastic automata networks," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 570-578.
    3. Cui, Lirong & Wu, Bei, 2019. "Extended Phase-type models for multistate competing risk systems," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 1-16.
    4. Shen, Jingyuan & Cui, Lirong & Ma, Yizhong, 2019. "Availability and optimal maintenance policy for systems degrading in dynamic environments," European Journal of Operational Research, Elsevier, vol. 276(1), pages 133-143.

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