Eryilmaz, Serkan2024-07-052024-07-0520120167-715210.1016/j.spl.2011.10.0222-s2.0-81055137671https://doi.org/10.1016/j.spl.2011.10.022https://hdl.handle.net/20.500.14411/1371Eryilmaz, Serkan/0000-0002-2108-1781According 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. (C) 2011 Elsevier B.V. All rights reserved.eninfo:eu-repo/semantics/closedAccessGeometric distribution of order kPoisson processRunsShock modelArticle