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Article Citation - WoS: 75Citation - Scopus: 77Reliability and Optimal Replacement Policy for an Extreme Shock Model With a Change Point(Elsevier Sci Ltd, 2019) Eryilmaz, Serkan; Kan, CihangirAn extreme shock model when there is a change in the distribution of the magnitudes of shocks is defined and studied. Such a model is useful in practice since a sudden change in environmental conditions may cause a larger shock. In particular, the reliability and mean time to failure of the system is obtained by assuming that the times between arrivals of shocks follow phase-type distribution. The optimal replacement policy that is based on a control limit is also proposed. The results are illustrated when the number of shocks until the change point follows geometric distribution.Article Citation - WoS: 13Citation - Scopus: 13Reliability Assessment of a Discrete Time Cold Standby Repairable System(Springer, 2021) Kan, Cihangir; Eryilmaz, SerkanThis paper is concerned with the study of a discrete time repairable system consisting of one active and one standby component. The lifetime and repair time are assumed to have discrete phase-type distributions. The system's lifetime is represented as a compound random variable. A matrix-based expression for the probability generating function of the system's lifetime is obtained based on the phase characteristics of lifetime and repair time distributions. The probability generating function is then used to obtain the distribution of the system's lifetime. Reliability and hazard rate functions are computed and evaluated for some particular choices of lifetime and repair time distributions. The limiting behavior of the hazard rates is also investigated.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: 17Citation - Scopus: 25On the Theoretical Distribution of the Wind Farm Power When There Is a Correlation Between Wind Speed and Wind Turbine Availability(Elsevier Sci Ltd, 2020) Kan, Cihangir; Devrim, Yilser; Eryilmaz, SerkanIt is important to elicit information about the potential power output of a wind turbine and a wind farm consisting of specified number of wind turbines before installation of the turbines. Such information can be used to estimate the potential power output of the wind farm which will be built in a specific region. The output power of a wind turbine is affected by two factors: wind speed and turbine availability. As shown in the literature, the correlation between wind speed and wind turbine availability has an impact on the output of a wind farm. Thus, the probability distribution of the power produced by the farm depending on the wind speed distribution and turbine availability can be effectively used for planning and risk management. In this paper, the theoretical distribution of the wind farm power is derived by considering the dependence between turbine availability and the wind speed. The theoretical results are illustrated for real wind turbine reliability and wind speed data.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.
