Generalized δ-shock model via runs

Serkan Eryılmaz

Statistics & Probability Letters, 2012, vol. 82, issue 2, 326-331

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.

Keywords: Geometric distribution of order k; Poisson process; Runs; Shock model (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spl.2011.10.022

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