IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v93y2008i11p1650-1657.html
   My bibliography  Save this article

Modelling a reliability system governed by discrete phase-type distributions

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832008000367
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2008.01.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:93:y:2008:i:11:p:1650-1657. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.