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L z -Transform for a Discrete-State Continuous-Time Markov Process and its Applications to Multi-State System Reliability

In: Recent Advances in System Reliability

Author

Listed:
  • Anatoly Lisnianski

    (The Israel Electric Corporation Ltd.)

Abstract

During last years a specific approach called the universal generating function (UGF) technique has been widely applied to MSS reliability analysis. The UGF technique allows one to algebraically find the entire MSS performance distribution through the performance distributions of its elements. However, the main restriction of this powerful technique is that theoretically it may be only applied to random variables and, so, concerning MSS reliability, it operates with only steady-states performance distributions. In order to extend the UGF technique application to dynamic MSS reliability analysis the paper introduces a special transform for a discrete-states continuous-time Markov process that is called L Z -transform. The transform was mathematically defined, its main properties were studied, and numerical example illustrating its benefits for dynamic MSS reliability assessment is presented.

Suggested Citation

  • Anatoly Lisnianski, 2012. "L z -Transform for a Discrete-State Continuous-Time Markov Process and its Applications to Multi-State System Reliability," Springer Series in Reliability Engineering, in: Anatoly Lisnianski & Ilia Frenkel (ed.), Recent Advances in System Reliability, chapter 0, pages 79-95, Springer.
    • Handle: RePEc:spr:ssrchp:978-1-4471-2207-4_6
    DOI: 10.1007/978-1-4471-2207-4_6
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    Cited by:

    1. Huan Yu & Jun Yang & Yu Zhao, 2018. "Reliability of nonrepairable phased-mission systems with common bus performance sharing," Journal of Risk and Reliability, , vol. 232(6), pages 647-660, December.
    2. Ding, Yi & Cui, Wenqi & Zhang, Shujun & Hui, Hongxun & Qiu, Yiwei & Song, Yonghua, 2019. "Multi-state operating reserve model of aggregate thermostatically-controlled-loads for power system short-term reliability evaluation," Applied Energy, Elsevier, vol. 241(C), pages 46-58.
    3. Yu, Huan & Yang, Jun & Mo, Huadong, 2014. "Reliability analysis of repairable multi-state system with common bus performance sharing," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 90-96.
    4. George-Williams, Hindolo & Patelli, Edoardo, 2016. "A hybrid load flow and event driven simulation approach to multi-state system reliability evaluation," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 351-367.
    5. Eryilmaz, Serkan & Rıza Bozbulut, Ali, 2014. "An algorithmic approach for the dynamic reliability analysis of non-repairable multi-state weighted k-out-of-n:G system," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 61-65.
    6. Ossai, Chinedu I., 2019. "Remaining useful life estimation for repairable multi-state components subjected to multiple maintenance actions," Reliability Engineering and System Safety, Elsevier, vol. 182(C), pages 142-151.
    7. Eryilmaz, Serkan, 2015. "Dynamic assessment of multi-state systems using phase-type modeling," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 71-77.

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