IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v24y2022i1d10.1007_s11009-021-09847-9.html
   My bibliography  Save this article

Assessment of Shock Models for a Particular Class of Intershock Time Distributions

Author

Listed:
  • Coskun Kus

    (Selcuk University)

  • Altan Tuncel

    (Kirikkale University)

  • Serkan Eryilmaz

    (Atilim University)

Abstract

In this paper, delta and extreme shock models and a mixed shock model which combines delta-shock and extreme shock models are studied. In particular, the interarrival times between successive shocks are assumed to belong to a class of matrix-exponential distributions which is larger than the class of phase-type distributions. The Laplace -Stieltjes transforms of the systems’ lifetimes are obtained in a matrix form. Survival functions of the systems are approximated based on the Laplace-Stieltjes transforms. The results are applied for the reliability evaluation of a certain repairable system consisting of two components.

Suggested Citation

  • Coskun Kus & Altan Tuncel & Serkan Eryilmaz, 2022. "Assessment of Shock Models for a Particular Class of Intershock Time Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 213-231, March.
  • Handle: RePEc:spr:metcap:v:24:y:2022:i:1:d:10.1007_s11009-021-09847-9
    DOI: 10.1007/s11009-021-09847-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-021-09847-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s11009-021-09847-9?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.

    References listed on IDEAS

    as
    1. Markos V. Koutras & Serkan Eryilmaz, 2017. "Compound Geometric Distribution of Order k," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 377-393, June.
    2. 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.
    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. Parvardeh, A. & Balakrishnan, N., 2015. "On mixed δ-shock models," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 51-60.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Xiaoyue Wang & Ru Ning & Xian Zhao, 2023. "Generalized mixed shock model for multi-component systems in the shock environment with a change point," Journal of Risk and Reliability, , vol. 237(4), pages 619-635, August.
    2. Jewgeni H. Dshalalow & Hend Aljahani, 2023. "Discrete and Continuous Operational Calculus in N-Critical Shocks Reliability Systems with Aging under Delayed Information," Mathematics, MDPI, vol. 11(16), pages 1-27, August.
    3. Lyu, Hao & Qu, Hongchen & Yang, Zaiyou & Ma, Li & Lu, Bing & Pecht, Michael, 2023. "Reliability analysis of dependent competing failure processes with time-varying δ shock model," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    4. Chadjiconstantinidis, Stathis & Eryilmaz, Serkan, 2023. "Reliability of a mixed δ-shock model with a random change point in shock magnitude distribution and an optimal replacement policy," Reliability Engineering and System Safety, Elsevier, vol. 232(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dheeraj Goyal & Nil Kamal Hazra & Maxim Finkelstein, 2022. "On the Time-Dependent Delta-Shock Model Governed by the Generalized PóLya Process," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1627-1650, September.
    2. Xian Zhao & Yanbo Song & Xiaoyue Wang & Zhiyue Lv, 2022. "Distributions of $$({k}_{1},{k}_{2},\dots ,{k}_{m})$$ ( k 1 , k 2 , ⋯ , k m ) -runs with Multi-state Trials," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2689-2702, December.
    3. Stathis Chadjiconstantinidis & Altan Tuncel & Serkan Eryilmaz, 2023. "Α new mixed δ-shock model with a change in shock distribution," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 491-509, October.
    4. Chen, Yunxia & Zhang, Wenbo & Xu, Dan, 2019. "Reliability assessment with varying safety threshold for shock resistant systems," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 49-60.
    5. Mohsen Bohlooli-Zefreh & Majid Asadi & Afshin Parvardeh, 2021. "On the reliability and optimal maintenance of systems under a generalized mixed δ -shock model," Journal of Risk and Reliability, , vol. 235(5), pages 909-922, October.
    6. repec:bpj:demode:v:6:y:2018:i:1:p:131-138:n:8 is not listed on IDEAS
    7. Vasileios M. Koutras & Markos V. Koutras & Spiros D. Dafnis, 2022. "A Family of Induced Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1833-1848, September.
    8. Yu, Xiaoyun & Hu, Linmin & Ma, Mengrao, 2023. "Reliability measures of discrete time k-out-of-n: G retrial systems based on Bernoulli shocks," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    9. 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.
    10. Mohsen Bohlooli-Zefreh & Afshin Parvardeh & Majid Asadi, 2023. "On the occurrence time of an extreme damage in a general shock model," Journal of Risk and Reliability, , vol. 237(6), pages 1100-1113, December.
    11. Eryilmaz, Serkan, 2017. "δ-shock model based on Polya process and its optimal replacement policy," European Journal of Operational Research, Elsevier, vol. 263(2), pages 690-697.
    12. Eryilmaz, Serkan, 2021. "Revisiting discrete time age replacement policy for phase-type lifetime distributions," European Journal of Operational Research, Elsevier, vol. 295(2), pages 699-704.
    13. Vasileios M. Koutras & Markos V. Koutras, 2020. "Exact Distribution of Random Order Statistics and Applications in Risk Management," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1539-1558, December.
    14. Eryilmaz, Serkan & Unlu, Kamil Demirberk, 2023. "A new generalized δ-shock model and its application to 1-out-of-(m+1):G cold standby system," Reliability Engineering and System Safety, Elsevier, vol. 234(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:spr:metcap:v:24:y:2022:i:1:d:10.1007_s11009-021-09847-9. 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.

    If CitEc recognized a bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.