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Article Citation - WoS: 1Citation - Scopus: 2On the First Time of Ruin in Two-Dimensional Discrete Time Risk Model With Dependent Claim Occurrences(Taylor & Francis inc, 2018) Eryilmaz, SerkanThis article is concerned with a two-dimensional discrete time risk model based on exchangeable dependent claim occurrences. In particular, we obtain a recursive expression for the finite time non ruin probability under such a dependence among claim occurrences. For an illustration, we define a bivariate compound beta-binomial risk model and present numerical results on this model by comparing the corresponding results of the bivariate compound binomial risk model.Article Citation - WoS: 61Citation - 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: 66Citation - Scopus: 76Multivariate Copula Based Dynamic Reliability Modeling With Application To Weighted-k-out-of-n< Systems of Dependent Components(Elsevier, 2014) Eryilmaz, SerkanIn this paper, a multivariate copula based modeling methodology for dynamic reliability modeling of weighted-k-out-of-n systems is applied. The system under consideration is assumed to have n dependent components each having its own weight. It has a performance level of at least k when the total weight of operating components is k or above. Copula based expressions for the survival function and mean time to failure of such a system are obtained. Extensive numerical results are presented for Clayton and Gumbel type copulas. The behavior of survival function and mean time to failure are investigated with respect to the value of Kendall's correlation coefficient. (C) 2014 Elsevier Ltd. All rights reserved.Article Citation - WoS: 13Citation - Scopus: 14On Mean Residual Life of Discrete Time Multi-State Systems(Nctu-national Chiao Tung Univ Press, 2013) Eryilmaz, SerkanThe mean residual life function is an important characteristic in reliability and survival analysis. Although many papers have studied the mean residual life of binary systems, the study of this characteristic for multi-state systems is new. In this paper, we study mean residual life of discrete time multi-state systems that have M + 1 states of working efficiency. In particular, we consider two different definitions of mean residual life function and evaluate them assuming that the degradation in multi-state system follows a Markov process.Article Citation - WoS: 11Citation - Scopus: 11Reliability 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: 22Citation - Scopus: 24Computing reliability indices of repairable systems via signature(Elsevier Science Bv, 2014) Eryilmaz, SerkanThe purpose of this paper is to show the usefulness of system signature for computing some important reliability indices of repairable systems. In particular, we obtain signature-based expressions for stationary availability, rate of occurrence of failure, and mean time to the first failure of repairable systems. Using these expressions we compute corresponding reliability indices of all systems with three and four components. Computational results are also presented for consecutive-k-within-m-out-of-n:F and m-consecutive-k-out-of-n:F systems. (C) 2013 Elsevier B.V. All rights reserved.Article Citation - WoS: 4Citation - Scopus: 4On compound sums under dependence(Elsevier, 2017) Eryilmaz, SerkanIn this paper, we study the compound random variable S = Sigma(N)(t-1) Y-t when there is a dependence between a random variable N and a sequence of random variables {Y-t}(t >= 1). Such a compound random variable has been found to be useful in several fields including actuarial science, risk management, and reliability. In particular, we develop some results on distributional properties of the random variable S when N is a phase-type random variable that is defined on a sequence of binary trials and depends on {Y-t}(t >= 1). We "present illustrative examples and an application for the use of results in actuarial science. (C) 2016 Elsevier B.V. All rights reserved.Article Citation - WoS: 23Citation - Scopus: 26Lifetime 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: 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.
