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Modelling a reliability system governed by discrete phase-type distributions

Author

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  • Ruiz-Castro, Juan Eloy
  • Pérez-Ocón, Rafael
  • Fernández-Villodre, Gemma

Abstract

We present an n-system with one online unit and the others in cold standby. There is a repairman. When the online fails it goes to repair, and instantaneously a standby unit becomes the online one. The operational and repair times follow discrete phase-type distributions. Given that any discrete distribution defined on the positive integers is a discrete phase-type distribution, the system can be considered a general one. A model with unlimited number of units is considered for approximating a system with a great number of units. We show that the process that governs the system is a quasi-birth-and-death process. For this system, performance reliability measures; the up and down periods, and the involved costs are calculated in a matrix and algorithmic form. We show that the discrete case is not a trivial case of the continuous one. The results given in this paper have been implemented computationally with Matlab.

Suggested Citation

  • Ruiz-Castro, Juan Eloy & Pérez-Ocón, Rafael & Fernández-Villodre, Gemma, 2008. "Modelling a reliability system governed by discrete phase-type distributions," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1650-1657.
    • Handle: RePEc:eee:reensy:v:93:y:2008:i:11:p:1650-1657
    DOI: 10.1016/j.ress.2008.01.005
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    Cited by:

    1. Alkaff, Abdullah, 2021. "Discrete time dynamic reliability modeling for systems with multistate components," Reliability Engineering and System Safety, Elsevier, vol. 209(C).
    2. Li, Jingkui & Lu, Yuze & Liu, Xiaona & Jiang, Xiuhong, 2023. "Reliability analysis of cold-standby phased-mission system based on GO-FLOW methodology and the universal generating function," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    3. Moghaddass, Ramin & Zuo, Ming J. & Wang, Wenbin, 2011. "Availability of a general k-out-of-n:G system with non-identical components considering shut-off rules using quasi-birth–death process," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 489-496.

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