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Generalized δ-shock model via runs

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  • Eryılmaz, Serkan
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 2 ()
    Pages: 326-331

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:2:p:326-331

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    Related research

    Keywords: Geometric distribution of order k; Poisson process; Runs; Shock model;

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    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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