IDEAS home Printed from https://ideas.repec.org/a/sae/risrel/v234y2020i1p138-150.html
   My bibliography  Save this article

A new δ-shock model for systems subject to multiple failure types and its optimal order-replacement policy

Author

Listed:
  • Yi Jiang

Abstract

In this article, a generalized δ -shock model with multi-failure thresholds is studied. For the new model, the system fails depending on the interval times between two consecutive shocks which arrive according to a Poisson process. The shorter interval times may cause more serious failures and thus result in longer down times and more costs for repair. Assuming that the repair is imperfect, an order-replacement policy N is adopted. Explicitly, the spare system for replacement is ordered at the end of ( N  – 1)th repair and the aging system is replaced at the N th failure or at an unrepairable failure, whichever occurs first. In addition, the system must meet the requirement of availability, that is, the long-run average operating time per unit time should not be lower than a certain level. The average cost rate C ( N ) and the stationary availability A ( N ) are derived analytically. Some convergence properties of A ( N ) and C ( N ) are also investigated. The optimal order-replacement policy N * can be obtained numerically with the constraint of availability. Finally, an illustrative example is given and some sensitivity analyses are conducted to demonstrate the proposed shock model.

Suggested Citation

  • Yi Jiang, 2020. "A new δ-shock model for systems subject to multiple failure types and its optimal order-replacement policy," Journal of Risk and Reliability, , vol. 234(1), pages 138-150, February.
  • Handle: RePEc:sae:risrel:v:234:y:2020:i:1:p:138-150
    DOI: 10.1177/1748006X19865801
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/1748006X19865801
    Download Restriction: no

    References listed on IDEAS

    as
    1. Rafiee, Koosha & Feng, Qianmei & Coit, David W., 2017. "Reliability assessment of competing risks with generalized mixed shock models," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 1-11.
    2. Lam, Yeh & Zhang, Yuan Lin & Zheng, Yao Hui, 2002. "A geometric process equivalent model for a multistate degenerative system," European Journal of Operational Research, Elsevier, vol. 142(1), pages 21-29, October.
    3. Serkan Eryilmaz & Konul Bayramoglu, 2014. "Life behavior of $$\delta $$ δ -shock models for uniformly distributed interarrival times," Statistical Papers, Springer, vol. 55(3), pages 841-852, August.
    4. Gut, Allan & Hüsler, Jürg, 2005. "Realistic variation of shock models," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 187-204, September.
    Full references (including those not matched with items on IDEAS)

    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:sae:risrel:v:234:y:2020:i:1:p:138-150. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (SAGE Publications). General contact details of provider: .

    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.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.