06036311

j

06036311 Ery{\i}lmaz, Serkan Generalized $\delta$-shock model via runs. Stat. Probab. Lett. 82, No. 2, 326-331 (2012). 2012 Elsevier Science B.V. (North-Holland), Amsterdam EN geometric distribution of order $k$ Poisson process runs shock model

doi:10.1016/j.spl.2011.10.022

Summary: According to the $\delta $-shock model, the system fails when the time between two consecutive shocks falls below a fixed threshold $\delta $. 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 $\delta $. 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.