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Article Citation - WoS: 45Citation - Scopus: 51On 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: 25Citation - Scopus: 28Lifetime of Multistate k-out-of-n< Systems(Wiley-blackwell, 2014) Eryilmaz, SerkanA multistate k-out-of-n system model is an extension of binary k-out-of-n system model by allowing multiple performance levels for the system and its components. Various definitions of multistate k-out-of-n system model have been proposed in the literature. Previous studies on these systems mostly focus on reliability evaluation algorithms. The present paper investigates the lifetimes of multistate systems. In particular, the lifetimes of two different multistate k-out-of-n system models are represented in terms of order statistics, and bounds and approximations are presented using these representations. The results are illustrated for a multistate system whose components' degradation occurs according to a Markov process. Copyright (C) 2013 John Wiley & Sons, Ltd.Article Citation - WoS: 9Citation - Scopus: 11Reliability of the Two-Unit Priority Standby System Revisited(Sage Publications Ltd, 2022) Eryilmaz, Serkan; Finkelstein, MaximThis paper deals with reliability assessment of the repairable two-unit cold standby system when the first, main unit has the better performance level than the second one. Therefore, after its repair, the main unit is always switched into operation. The new Laplace transform representation for the system's lifetime is obtained for arbitrary operation and repair time distributions of the units. For some particular cases, the Laplace transform of the system is shown to be rational, which enables the use of the matrix-exponential distributions for obtaining relevant reliability indices. The discrete setup of the model is also considered through the corresponding matrix-geometric distributions, which are the discrete analogs of the matrix-exponential distributions.Article Citation - WoS: 17Citation - Scopus: 16A Study on Reliability of Coherent Systems Equipped With a Cold Standby Component(Springer Heidelberg, 2014) Eryilmaz, SerkanIn this paper, we investigate the effect of a single cold standby component on the performance of a coherent system. In particular, we focus on coherent systems which may fail at the time of the first component failure in the system. We obtain signature based expressions for the survival function and mean time to failure of the coherent systems satisfying the abovementioned property.Article Citation - WoS: 7Citation - Scopus: 8Modeling Systems With Two Dependent Components Under Bivariate Shock Models(Taylor & Francis inc, 2019) Eryilmaz, SerkanSeries and parallel systems consisting of two dependent components are studied under bivariate shock models. The random variables N-1 and N-2 that represent respectively the number of shocks until failure of component 1 and component 2 are assumed to be dependent and phase-type. The times between successive shocks are assumed to follow a continuous phase-type distribution, and survival functions and mean time to failure values of series and parallel systems are obtained in matrix forms. An upper bound for the joint survival function of the components is also provided under the particular case when the times between shocks follow exponential distribution.Article Citation - WoS: 7Citation - Scopus: 8Analysis of the Two-Unit Cold Standby Repairable System With Damage and Repair Time Dependency Via Matrix-Exponential Distributions(Taylor & Francis Ltd, 2021) Kus, Coskun; Eryilmaz, SerkanIn this paper, two-unit standby repairable system is studied via matrix-exponential distributions. The system under concern consists of one active and one standby components, and fails if either a damage size upon the failure of the active component is larger than a repair limit or the repair time of the failed unit exceeds the lifetime of the active unit, whichever happens first. Under the assumption that the damage size and repair time are statistically dependent, the Laplace transform of the system's lifetime is obtained. The Laplace transform is shown to be rational under particular cases, and the reliability evaluation of the system is performed via well-known distributional properties of the matrix-exponential distributions. The problem of estimating the unknown parameters of the operation time and repair time distributions is also discussed based on system's lifetime data.Article Citation - WoS: 66Citation - Scopus: 77Generalized 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: 23Citation - Scopus: 26Optimization Problems for a Parallel System With Multiple Types of Dependent Components(Elsevier Sci Ltd, 2020) Eryilmaz, Serkan; Ozkut, MuratThis paper is concerned with two optimization problems for a parallel system that consists of dependent components. First, the problem of finding the number of elements in the system that minimizes the mean cost rate of the system is considered. The second problem is concerned with the optimal replacement time of the system. Previous work assumes that the components are independent. We discuss the impact of dropping this assumption. In particular, we numerically examine how the dependence between the components affects the optimal number of units and replacement time for the system which minimize mean cost rates. We first consider the case when the components are exchangeable and dependent, i.e. the system consists of single type of dependent components. Subsequently, we consider a system that consists of multiple types of dependent components. Comparative numerical results are presented for particularly chosen dependence models.Article Citation - WoS: 19Citation - Scopus: 21Mean Instantaneous Performance of a System With Weighted Components That Have Arbitrarily Distributed Lifetimes(Elsevier Sci Ltd, 2013) Eryilmaz, SerkanThere are various systems consisting of components which may have different contribution to the performance of the system. Such systems can be modeled systems with weighted components. In this paper, we study the mean instantaneous performance of this type of systems after successive component failures. The mean instantaneous performance is a useful characteristic to take preventive action about the system. In particular, we obtain explicit expressions for the mean instantaneous performance of a system with weighted components that have arbitrarily distributed lifetimes. We illustrate the results when the lifetime distribution of components follow proportional hazard model. Some further results are also presented for the components having exponential lifetime distribution. (C) 2013 Elsevier Ltd. All rights reserved.Article Citation - WoS: 12Citation - Scopus: 13A New Mixed Δ-Shock Model With a Change in Shock Distribution(Springer, 2023) Chadjiconstantinidis, Stathis; Tuncel, Altan; Eryilmaz, SerkanIn this paper, reliability properties of a system that is subject to a sequence of shocks are investigated under a particular new change point model. According to the model, a change in the distribution of the shock magnitudes occurs upon the occurrence of a shock that is above a certain critical level. The system fails when the time between successive shocks is less than a given threshold, or the magnitude of a single shock is above a critical threshold. The survival function of the system is studied under both cases when the times between shocks follow discrete distribution and when the times between shocks follow continuous distribution. Matrix-based expressions are obtained for matrix-geometric discrete intershock times and for matrix-exponential continuous intershock times, as well.
