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Article Citation - WoS: 43Citation - Scopus: 50On the lifetime behavior of a discrete time shock model(Elsevier, 2013) Eryilmaz, SerkanIn this article, we study a shock model in which the shocks occur according to a binomial process, i.e. the interarrival times between successive shocks follow a geometric distribution with mean 1/p. According to the model, the system fails when the time between two consecutive shocks is less than a prespecified level. This is the discrete time version of the so-called delta-shock model which has been previously studied for the continuous case. We obtain the probability mass function and probability generating function of the system's lifetime. We also present an extension of the results to the case where the shock occurrences are dependent in a Markovian fashion. (C) 2012 Elsevier B.V. All rights reserved.Article Citation - WoS: 60Citation - Scopus: 64Computing Optimal Replacement Time and Mean Residual Life in Reliability Shock Models(Pergamon-elsevier Science Ltd, 2017) Eryilmaz, SerkanIn this paper, matrix-based methods are presented to compute the optimal replacement time and mean residual lifetime of a system under particular class of reliability shock models. The times between successive shocks are assumed to have a common continuous phase-type distribution. The system's lifetime is represented as a compound random variable and some properties of phase-type distributions are utilized. Extreme shock model, run shock model, and generalized extreme shock model are shown to be the members of this class. Graphical illustrations and numerical examples are presented for the run shock model when the interarrival times between shocks follow Erlang distribution. (C) 2016 Elsevier Ltd. All rights reserved.Article Citation - WoS: 9Citation - Scopus: 10Reliability and Performance Evaluation of Weighted K-out-of- N :g System Consisting of Components With Discrete Lifetimes(Elsevier Sci Ltd, 2024) Eryilmaz, SerkanFor the k-out-of-n n system consisting of components that have different weights, the system is in a good state if the total weight of working components is at least k . Such a system is known to be weighted k-out-of- n :G system. Although the weighted k-out-of-n n system that has continuously distributed components' lifetimes has been extensively studied, the discrete weighted k-out-of- n :G system has not been considered yet. The present paper fills this gap by modeling and analyzing the weighted k-out-of-n:G n :G system that consists of discretely distributed components' lifetimes. In particular, the behavior of the total capacity/weight of the system with respect to the component failures is evaluated. An optimization problem that is concerned with the determination of optimal number of spare components is also formulated by utilizing the mean lost capacity of the system.Article Citation - WoS: 20Citation - Scopus: 23A New Generalized Δ-Shock Model and Its Application To 1-out-of-(m+1):g Cold Standby System(Elsevier Sci Ltd, 2023) Eryilmaz, Serkan; Unlu, Kamil DemirberkAccording to the classical delta-shock model, the system failure occurs upon the occurrence of a new shock that arrives in a time length less than delta, a given positive value. In this paper, a new generalized version of the delta-shock model is introduced. Under the proposed model, the system fails if there are m shocks that arrive in a time length less than delta after a previous shock, m >= 1. The mean time to failure of the system is approximated for both discretely and continuously distributed intershock time distributions. The usefulness of the model is also shown to study 1-out-of-(m + 1):G cold standby system. Illustrative numerical results are presented for geometric, exponential, discrete and continuous phase-type intershock time distributions.Article Citation - WoS: 55Citation - Scopus: 59Assessment of a Multi-State System Under a Shock Model(Elsevier Science inc, 2015) Eryilmaz, SerkanA system is subject to random shocks over time. Let c(1) and c(2) be two critical levels such that c(1) < c(2). A shock with a magnitude between c(1) and c(2) has a partial damage on the system, and the system transits into a lower partially working state upon the occurrence of each shock in (c(1), c(2)). A shock with a magnitude above c(2) has a catastrophic affect on the system and it causes a complete failure. Such a shock model creates a multi-state system having random number of states. The lifetime, the time spent by the system in a perfect functioning state, and the total time spent by the system in partially working states are defined and their survival functions are derived when the interarrival times between successive shocks follow phasetype distribution. (C) 2015 Elsevier Inc. 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.
