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Generalized δ-shock model via runs


  • Eryılmaz, Serkan


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

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    References listed on IDEAS

    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.
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