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Article Citation - WoS: 11Citation - Scopus: 10Modeling of Claim Exceedances Over Random Thresholds for Related Insurance Portfolios(Elsevier, 2011) Eryilmaz, Serkan; Gebizlioglu, Omer L.; Tank, FatihLarge claims in an actuarial risk process are of special importance for the actuarial decision making about several issues like pricing of risks, determination of retention treaties and capital requirements for solvency. This paper presents a model about claim occurrences in an insurance portfolio that exceed the largest claim of another portfolio providing the same sort of insurance coverages. Two cases are taken into consideration: independent and identically distributed claims and exchangeable dependent claims in each of the portfolios. Copulas are used to model the dependence situations. Several theorems and examples are presented for the distributional properties and expected values of the critical quantities under concern. (C) 2011 Elsevier B.V. All rights reserved.Article Citation - WoS: 62Citation - Scopus: 69Estimation in Coherent Reliability Systems Through Copulas(Elsevier Sci Ltd, 2011) Eryilmaz, SerkanThe problem of estimating the parameter of a common distribution of components' lifetimes from system's lifetime data is of interest and importance in reliability engineering. The present paper deals with this problem when the common component distribution is exponential with mean it and the lifetimes of components have an exchangeable joint distribution which is constructed by the help of Archimedean copula. In particular we obtain moment estimator of p for Clayton and Ali-Mikhail-Haq copulas. We illustrate the findings of the paper for a special class of coherent systems called consecutive k-within-m-out-of-n:F system. A simulation study is performed to investigate the properties of the moment estimator. The method presented in this paper can be applied to all coherent systems. (C) 2010 Elsevier Ltd. All rights reserved.Article Citation - Scopus: 1The Distribution of Wind Power from a Dispersed Array of Wind Turbine Generators and Its Reliability Based Applications(Elsevier, 2026) Eryilmaz, Serkan; Kan, Cihangir; Devrim, YilserIn this paper, the probability distribution of wind power from a dispersed array of wind turbine sites is studied considering forced outage rates of wind turbines. The wind speeds at distinct sites are assumed to be dependent and the dependence is modeled by copulas. In particular, the probability distribution of the aggregate power from two sites is exactly derived. The probability distribution of the aggregate power is also derived under the particular case when site 1 consists of n1 identical wind turbines of type 1 and site 2 consists of n2 identical wind turbines of type 2. Numerical results are presented to illustrate the theoretical findings for a chosen copula function.Article Citation - WoS: 21Citation - Scopus: 24Optimization 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: 18Citation - Scopus: 21Modeling Dependence Between Two Multi-State Components Via Copulas(Ieee-inst Electrical Electronics Engineers inc, 2014) Eryilmaz, SerkanModeling statistical dependence between two systems or components is an important problem in reliability theory. Such a problem has been well studied for binary systems and components. In the present paper, we provide a way for modeling s-dependence between two multi-state components. Our method is based on the use of copulas which are very popular for modeling s-dependence. We obtain expressions for the joint state probabilities of the two components, and illustrate the results for the case when the degradation in both components follows a Markov process.Article Citation - WoS: 26Citation - Scopus: 28A Reliability Model for a Three-State Degraded System Having Random Degradation Rates(Elsevier Sci Ltd, 2016) Eryilmaz, SerkanFor degraded multi-state systems, it has been assumed in the literature that, for any given system, the instantaneous degradation rates are fixed. This paper attempts to study a three-state degraded system that have random degradation rates among its states. In particular, a reliability model for such a three state system is presented assuming that the degradation rates are random and statistically dependent. The dependence is modeled by copulas, and dynamic reliability analysis of the system is performed. Graphical illustrations are provided, and comparisons are made with the corresponding results for the classical fixed rates model. (C) 2016 Elsevier Ltd. All rights reserved.Article Citation - WoS: 65Citation - Scopus: 75Multivariate 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: 36Citation - Scopus: 39Reliability Based Modeling and Analysis for a Wind Power System Integrated by Two Wind Farms Considering Wind Speed Dependence(Elsevier Sci Ltd, 2020) Eryilmaz, Serkan; Kan, CihangirIntegrating multiple wind farms into power systems may reduce the fluctuation in total power output of wind farms and hence it decreases the system risk resulting from the wind speed variability. In this paper, a wind power system consisting of two wind farms is modeled and analyzed considering the dependence between wind speeds at two sites. In particular, the system is modeled as a threshold system and reliability values of wind turbines are also taken into account in capacity based calculations. The results are illustrated for the available bivariate wind speed data in the literature.
