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Article Citation - WoS: 61Citation - Scopus: 72Generalized δ-shock model via runs(Elsevier Science Bv, 2012) Eryilmaz, SerkanAccording 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.Article Citation - WoS: 55Citation - Scopus: 60Reliability Evaluation of a System Under a Mixed Shock Model(Elsevier Science Bv, 2019) Eryilmaz, Serkan; Tekin, MustafaA new mixed shock model is introduced and studied. According to the model, for two fixed critical values d(1) and d(2) such that d(1) < d(2), the system under concern fails upon the occurrence of k consecutive shocks of size at least d(1) or a single large shock of size at least d(2). The new model combines run and extreme shock models. Reliability properties of the system are studied under two cases: when the interarrival time X-i between the (i - 1)th and ith shock, and the magnitude of the ith shock Y-i are independent for all i, and when the interarrival time between the (i - 1)th and ith shock, and the magnitude of the ith shock are dependent for all i. (C) 2018 Elsevier B.V. All rights reserved.
