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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: 1A Class of Shock Models for a System That Is Equipped With a Protection Block With an Application to Wind Turbine Reliability(Wiley, 2025) Eryilmaz, SerkanThis paper studies a class of shock models for a system that is equipped with a protection block that has its own failure rate. Under the considered class, the system exposed to shocks at random times is protected by the protection block, and the probability of the shock damaging the system varies depending on whether the protection block operates or not. The system failure criteria is defined based on the pattern of the critical/damaging shocks. Exact expressions for the reliability and mean time to failure of the system are obtained, and detailed computations are presented for the run shock model, which is included in the class. The application of the extreme shock model, which is included in the relevant class, to wind turbine reliability is also discussed.Article Citation - WoS: 36Citation - Scopus: 42Modeling and Analysis of Weighted-k-out-of-n< G System Consisting of Two Different Types of Components(Sage Publications Ltd, 2014) Eryilmaz, Serkan; Sarikaya, KadirThis article is concerned with the reliability analysis of a weighted-k-out-of-n: G system consisting of two types of components. The system is assumed to have n components which are classified into two groups with respect to their weight and reliability, and it is assumed to operate if the total weight of all working components exceeds a prespecified threshold k. The reliability properties of such a system are studied. The optimal values of the number of components in each group are also determined under a minimum required reliability by minimizing the total acquisition cost.Article Citation - WoS: 1Citation - Scopus: 2On the Lifetime of a Random Binary Sequence(Elsevier Science Bv, 2011) Eryilmaz, SerkanConsider a system with m elements which is used to fulfill tasks. Each task is sent to one element which fulfills a task and the outcome is either fulfillment of the task ("1") or the failure of the element ("0"). Initially, m tasks are sent to the system. At the second step, a complex of length m(1) is formed and sent to the system, where m(1) is the number of tasks fulfilled at the first step, and so on. The process continues until all elements fail and the corresponding waiting time defines the lifetime of the binary sequence which consists of "1" or "0". We obtain a recursive equation for the expected value of this waiting time random variable. (C) 2011 Elsevier B.V. All rights reserved.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: 4Citation - Scopus: 6On Profust Reliability of Coherent Systems: Signature-Based Expressions(Sage Publications Ltd, 2013) Eryilmaz, Serkan; Rouyendegh, Babak DaneshvarIn this article we study profust reliability of non-repairable coherent systems through the concept of system signature. We obtain explicit expressions for the profust reliability and mean time to fuzzy failure of coherent systems. We compute and present mean time to failure and mean time to fuzzy failure of all coherent systems with three and four components. Finally, we illustrate the results for a well known class of coherent systems called m-consecutive-k-out-of-n:F.Article Citation - WoS: 10Citation - Scopus: 11Consecutive k-out-of-n< Lines With a Change Point(Sage Publications Ltd, 2016) Eryilmaz, SerkanReliability analysis of consecutive k-out-of-n systems and their generalizations has attracted a great deal of attention in the literature. Such systems have been used to model telecommunication networks, oil pipeline systems, vacuum systems in accelerators, spacecraft relay stations, etc. In this paper, nonrecursive closed form equations are presented for the reliability functions and mean time to failure values of consecutive k-out-of-n systems consisting of two types of nonidentical components. The results are illustrated for reliability evaluation of oil pipeline system.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: 18Citation - Scopus: 21Component importance for linear consecutive-k-Out-of-n and m-Consecutive-k-Out-of-n systems with exchangeable components(Wiley-blackwell, 2013) Eryilmaz, SerkanMeasuring the relative importance of components in a mechanical system is useful for various purposes. In this article, we study Birnbaum and Barlow-Proschan importance measures for two frequently studied system designs: linear consecutive k -out-of- n and m -consecutive- k -out-of- n systems. We obtain explicit expressions for the component importance measures for systems consisting of exchangeable components. We illustrate the results for a system whose components have a Lomax type lifetime distribution. (c) 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013Article Citation - WoS: 6Citation - Scopus: 6Dynamic Reliability and Performance Evaluation of Multi-State Systems With Two Components(Hacettepe Univ, Fac Sci, 2011) Eryilmaz, Serkan; Industrial EngineeringIn this paper we study multi-state systems consisting of two components when the number of system states and the number of states of each component are the same, i.e. the systems under consideration are homogeneous multi-state systems. In particular we evaluate multi-state series and cold standby systems assuming that the degradation in their components follow a Markov process. The behaviour of systems with respect to degradation rates is also investigated in terms of stochastic ordering.
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