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Article Citation - WoS: 27Citation - Scopus: 31Generalized Extreme Shock Models and Their Applications(Taylor & Francis inc, 2020) Bozbulut, Ali Riza; Eryilmaz, SerkanIn the classical extreme shock model, the system fails due to a single catastrophic shock. In this paper, by assuming different arrival patterns of the shocks, two new types of extreme shock models are introduced. In these models, m possible sources may exert shocks on the system. Both models reduce to the classical extreme shock model when m = 1. Assuming phase-type distribution for times between successive shocks, we obtain survival functions and mean time to failure values of the system under new models. Two different optimization problems are also considered to determine the optimal number of sources.Article Citation - WoS: 8Citation - Scopus: 10Computing Reliability Indices of a Wind Power System Via Markov Chain Modelling of Wind Speed(Sage Publications Ltd, 2024) Eryilmaz, Serkan; Bulanik, Irem; Devrim, YilserStatistical modelling of wind speed is of great importance in the evaluation of wind farm performance and power production. Various models have been proposed in the literature depending on the corresponding time scale. For hourly observed wind speed data, the dependence among successive wind speed values is inevitable. Such a dependence has been well modelled by Markov chains. In this paper, the use of Markov chains for modelling wind speed data is discussed in the context of the previously proposed likelihood ratio test. The main steps for Markov chain based modelling methodology of wind speed are presented and the limiting distribution of the Markov chain is utilized to compute wind speed probabilities. The computational formulas for reliability indices of a wind farm consisting of a specified number of wind turbines are presented through the limiting distribution of a Markov chain. A case study that is based on real data set is also presented.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: 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: 26Citation - Scopus: 28Mean residual life of coherent systems consisting of multiple types of dependent components(Wiley, 2018) Eryilmaz, Serkan; Coolen, Frank P. A.; Coolen-Maturi, TahaniMean residual life is a useful dynamic characteristic to study reliability of a system. It has been widely considered in the literature not only for single unit systems but also for coherent systems. This article is concerned with the study of mean residual life for a coherent system that consists of multiple types of dependent components. In particular, the survival signature based generalized mixture representation is obtained for the survival function of a coherent system and it is used to evaluate the mean residual life function. Furthermore, two mean residual life functions under different conditional events on components' lifetimes are also defined and studied.Article Citation - WoS: 12Citation - Scopus: 14The Markov Discrete Time Δ-Shock Reliability Model and a Waiting Time Problem(Wiley, 2022) Chadjiconstantinidis, Stathis; Eryilmaz, Serkandelta-shock model is one of the widely studied shock models in reliability theory and applied probability. In this model, the system fails due to the arrivals of two consecutive shocks which are too close to each other. That is, the system breaks down when the time between two successive shocks falls below a fixed threshold delta. In the literature, the delta-shock model has been mostly studied by assuming that the time between shocks have continuous distribution. In the present paper, the discrete time version of the model is considered. In particular, a proper waiting time random variable is defined based on a sequence of two-state Markov dependent binary trials and the problem of finding the distribution of the system's lifetime is linked with the distribution of the waiting time random variable, and we study the joint as well as the marginal distributions of the lifetime, the number of shocks and the number of failures associated with these binary trials.Article Citation - WoS: 7Citation - Scopus: 9Reliability-Based Evaluation of Hybrid Wind-Solar Energy System(Sage Publications Ltd, 2021) Devrim, Yilser; Eryilmaz, SerkanIn this article, a hybrid system that consists of a specified number of wind turbines and solar modules is considered. In particular, the system is modeled using weightedk-out-of-nsystem which is also known as a threshold system in reliability literature. The system under concern consists ofn1identical wind turbines andn2identical solar modules, and each turbine and module can be in one of two states as working or failed. The probability that the entire hybrid system withn=n1+n2components produces power at minimum levelkis computed and evaluated. The importance of single-wind turbine and solar module is also calculated to measure which renewable energy component is more critical and important. Extensive numerical results that are based on real data set are presented to illustrate the model.Article Citation - WoS: 26Citation - Scopus: 28Reliability Assessment for Discrete Time Shock Models Via Phase-Type Distributions(Wiley, 2021) Eryilmaz, Serkan; Kan, CihangirIn this paper, particular shock models are studied for the case when the times between successive shocks and the magnitudes of shocks have discrete phase-type distributions. The well-known shock models such as delta shock model, extreme shock model, and the mixed shock model which is obtained by combining delta and extreme shock models are considered. The probability generating function and recursive equation for the distribution of the system's lifetime are obtained for the cases when the interarrival times between shocks and the magnitudes of shocks are independent and when they are dependent. System reliability is computed for particular interarrival distributions such as geometric, negative Binomial and generalized geometric distributions.Article Citation - WoS: 9Citation - Scopus: 10Coherent System With Standby Components(Wiley, 2018) Eryilmaz, Serkan; Erkan, T. ErmanA coherent system that consists of n independent components and equipped with r cold standby components is considered. A generalized mixture representation for the survival function of such a system is obtained, and it is used to examine reliability properties of the system. In particular, the effect of adding r standby components to a given set of original components is measured by computing mean time to failure of the system. The limiting behavior of the failure rate of the system is also examined using the mixture representation. The results are illustrated for a bridge system. A case study that is concerned with an oil pipeline system is also presented.Article Citation - WoS: 2Citation - Scopus: 2A New Extended δ-shock Model With the Consideration of Shock Magnitude(Wiley, 2024) Lorvand, Hamed; Eryilmaz, SerkanIn this article, a new delta$$ \delta $$-shock model that takes into account the magnitude of shocks is introduced and studied from reliability perspective. According to the new model, the system breaks down if either a shock after non-critical shock occurs in a time length less than delta 1$$ {\delta}_1 $$ or a shock after a critical shock occurs in a time length less than delta 2,$$ {\delta}_2, $$ where delta 1
