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Article Citation - WoS: 22Citation - Scopus: 23On Residual Lifetime of Coherent Systems After the rth Failure(Springer, 2013) Eryilmaz, SerkanIn this article we study the residual lifetime of a coherent system after the rth failure, i.e. the time elapsed from the rth failure until the system failure given that the system operates at the time of the rth failure. We provide a mixture representation for the corresponding residual lifetime distribution in terms of signature. We also obtain some stochastic ordering results for the residual lifetimes.Article Citation - WoS: 14Citation - Scopus: 14Discrete Time Series-Parallel System and Its Optimal Configuration(Elsevier Sci Ltd, 2021) Dembinska, Anna; Eryilmaz, SerkanThis paper is concerned with properties of series-parallel systems when the component lifetimes have discrete failure time distribution. For a series-parallel system consisting of a specified number of subsystems, we particularly focus on the number of failed components in each subsystem at the time when the system fails. Each subsystem is assumed to have identical components while different subsystems have different types of components. Assuming all components within the system are independent, we obtain exact distributions of the number of failed components at the time when the system fails. For the special case when the components have phase-type failure time distributions, matrix-based expressions are derived for the quantities under concern. The results are used to obtain optimal configuration of the series-parallel system which is replaced at failure.Article Citation - WoS: 14Citation - Scopus: 16Joint Reliability Importance in Coherent Systems With Exchangeable Dependent Components(Ieee-inst Electrical Electronics Engineers inc, 2016) Eryilmaz, Serkan; Oruc, Ozlem Ege; Oger, VolkanIn this paper, a general formula for computing the joint reliability importance of two components is obtained for a binary coherent system that consists of exchangeable dependent components. Using the new formula, the joint reliability importance can be easily calculated if the path sets of the system are known. As a special case, an expression for the joint reliability importance of two components is also obtained for a system consisting of independent and identical components. Illustrative numerical results are presented to compare the joint reliability importance of two components in the bridge system for the two cases when the components are exchangeable dependent and when the components are independent and identical.Article Citation - WoS: 5Citation - Scopus: 5On the Sums of Distributions of Order Statistics From Exchangeable Random Variables(Elsevier Science Bv, 2013) Eryilmaz, SerkanIn this paper, we obtain an expression between the sums of the marginal distributions of the order statistics and the common marginal distribution of an exchangeable random sequence. We also derive an expression between the sums of the joint distribution of two order statistics and the two dimensional joint distribution of an exchangeable random sequence. (C) 2013 Elsevier B.V. All rights reserved.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: 21Citation - Scopus: 29On Reliability Analysis of a Two-Dependent Series System With a Standby Unit(Elsevier Science inc, 2012) Eryilmaz, Serkan; Tank, FatihIn this paper we study a series system with two active components and a single cold standby unit. The two simultaneously working components are assumed to be dependent and this dependence is modeled by a copula function. In particular, we obtain an explicit expression for the mean time to failure of the system in terms of the copula function and marginal lifetime distributions. We also provide illustrative numerical results for different copula functions and marginal lifetime distributions. (c) 2012 Elsevier Inc. All rights reserved.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: 19Citation - Scopus: 21Revisiting Discrete Time Age Replacement Policy for Phase-Type Lifetime Distributions(Elsevier, 2021) Eryilmaz, SerkanFor a system (or unit) whose lifetime is measured by the number cycles, according to the discrete time age replacement policy, it is replaced preventively after n cycles or correctively at failure, whichever oc-curs first. In this paper, discrete time age replacement policy is revisited when the lifetime of the system is modeled by a discrete phase-type distribution. In particular, the necessary conditions for the unique and finite replacement cycle which minimizes the expected cost per unit of time are obtained. The nec-essary conditions are mainly based on the behavior of the hazard rate. The results are illustrated for some special discrete phase-type lifetime distributions. Computational results are also presented for the optimal replacement cycle under specific real life setups. (c) 2021 Elsevier B.V. All rights reserved.Article Citation - WoS: 60Citation - 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: 30Citation - Scopus: 34Discrete Time Shock Models in a Markovian Environment(Ieee-inst Electrical Electronics Engineers inc, 2016) Eryilmaz, SerkanThis paper deals with two different shock models in a Markovian environment. We study a system from a reliability point of view under these two shock models. According to the first model, the system fails if the cumulative shock magnitude exceeds a critical level, while in the second model the failure occurs when the cumulative effect of the shocks in consecutive periods is above a critical level. The shock occurrences over discrete time periods are assumed to be Markovian. We obtain expressions for the failure time distributions of the system under the two model. Illustrative computational results are presented for the survival probabilities and mean time to failure values of the system.
