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Article Citation - WoS: 11Citation - Scopus: 13Geometric Distribution of Order k With a Reward(Elsevier Science Bv, 2014) Eryilmaz, SerkanIn this paper, we introduce and study geometric distribution of order k with a reward. In a sequence of binary trials, suppose that each time a success occurs a random reward is received. The distribution of the number of trials until the sum of consecutive rewards is equal to or exceeds the level k is called geometric distribution of order k with a reward. We obtain expressions for the probability mass function of this distribution. (C) 2014 Elsevier B.V. All rights reserved.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: 4Citation - Scopus: 5A New Class of Lifetime Distributions(Elsevier Science Bv, 2016) Eryilmaz, SerkanIn this paper, a new class of lifetime distributions which is obtained by compounding arbitrary continuous lifetime distribution and discrete phase-type distribution is introduced. In particular, the class of exponential-phase type distributions is studied with some details. (C) 2016 Elsevier B.V. All rights reserved.
