IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v82y2012i2p326-331.html
   My bibliography  Save this article

Generalized δ-shock model via runs

Author

Listed:
  • Eryılmaz, Serkan

Abstract

According to the δ-shock model, the system fails when the time between two consecutive shocks falls below a fixed threshold δ. This model has a potential application in various fields such as inventory, insurance and system reliability. In this paper, we study run-related generalization of this model such that the system fails when k consecutive interarrival times are less than a threshold δ. The survival function and the mean value of the failure time of the system are explicitly derived for exponentially distributed interarrival times. We also propose a new combined shock model which considers both the magnitudes of successive shocks and the interarrival times.

Suggested Citation

  • Eryılmaz, Serkan, 2012. "Generalized δ-shock model via runs," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 326-331.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:2:p:326-331
    DOI: 10.1016/j.spl.2011.10.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715211003439
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2011.10.022?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. Philippou, Andreas N. & Georghiou, Costas & Philippou, George N., 1983. "A generalized geometric distribution and some of its properties," Statistics & Probability Letters, Elsevier, vol. 1(4), pages 171-175, June.
    Full references (including those not matched with items on IDEAS)

    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. Shmerling, Efraim, 2013. "A range reduction method for generating discrete random variables," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1094-1099.
    2. Sigeo Aki & Katuomi Hirano, 1994. "Distributions of numbers of failures and successes until the first consecutivek successes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 193-202, March.
    3. Drekic, Steve & Spivey, Michael Z., 2021. "On the number of trials needed to obtain k consecutive successes," Statistics & Probability Letters, Elsevier, vol. 176(C).
    4. Kolev Nikolai, 2005. "Run and Frequency Quotas Under Markovian Fashion and their Application in Risk Analysis," Stochastics and Quality Control, De Gruyter, vol. 20(1), pages 97-109, January.
    5. N. Balakrishnan & S. Mohanty & S. Aki, 1997. "Start-Up Demonstration Tests Under Markov Dependence Model with Corrective Actions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 155-169, March.
    6. Gómez-Déniz, Emilio & Sarabia, José María & Calderín-Ojeda, Enrique, 2011. "A new discrete distribution with actuarial applications," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 406-412, May.
    7. S. Aki & K. Hirano, 1989. "Estimation of parameters in the discrete distributions of order k," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(1), pages 47-61, March.
    8. Renault, Jérôme & Ziliotto, Bruno, 2020. "Hidden stochastic games and limit equilibrium payoffs," Games and Economic Behavior, Elsevier, vol. 124(C), pages 122-139.
    9. P. S. Chan & H. K. T. Ng & N. Balakrishnan, 2008. "Statistical inference for start-up demonstration tests with rejection of units upon observing d failures," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(8), pages 867-878.
    10. Aki, Sigeo, 2008. "Joint distributions of numbers of occurrences of a discrete pattern and weak convergence of an empirical process for the pattern," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1460-1473, August.
    11. N. Balakrishnan, 1997. "Joint Distributions of Numbers of Success-Runs and Failures Until the First Consecutive k Successes in a Binary Sequence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 519-529, September.
    12. Athanasios Rakitzis & Demetrios Antzoulakos, 2015. "Start-up demonstration tests with three-level classification," Statistical Papers, Springer, vol. 56(1), pages 1-21, February.
    13. Spiros Dafnis & Andreas Philippou & Demetrios Antzoulakos, 2012. "Distributions of patterns of two successes separated by a string of k-2 failures," Statistical Papers, Springer, vol. 53(2), pages 323-344, May.
    14. Kiyoshi Inoue & Sigeo Aki, 2018. "Joint distributions of numbers of runs of specified lengths on directed trees," Statistical Papers, Springer, vol. 59(1), pages 249-269, March.
    15. Qing Han & Sigeo Aki, 2000. "Waiting Time Problems in a Two-State Markov Chain," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(4), pages 778-789, December.
    16. A. N. Kumar & N. S. Upadhye, 2019. "Generalizations of distributions related to ( $$k_1,k_2$$ k 1 , k 2 )-runs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(2), pages 249-268, March.
    17. Kumar C. Satheesh & Nair B. Unnikrishnan, 2013. "Order k Version of the Alternative Hyper-Poisson Distribution," Stochastics and Quality Control, De Gruyter, vol. 28(2), pages 97-104, December.
    18. Muselli, Marco, 1996. "Simple expressions for success run distributions in bernoulli trials," Statistics & Probability Letters, Elsevier, vol. 31(2), pages 121-128, December.
    19. 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.
    20. Sigeo Aki & Katuomi Hirano, 1995. "Joint distributions of numbers of success-runs and failures until the first consecutivek successes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(2), pages 225-235, June.

    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:stapro:v:82:y:2012:i:2:p:326-331. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.