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Article Citation - WoS: 19Citation - Scopus: 21Mean Instantaneous Performance of a System With Weighted Components That Have Arbitrarily Distributed Lifetimes(Elsevier Sci Ltd, 2013) Eryilmaz, SerkanThere are various systems consisting of components which may have different contribution to the performance of the system. Such systems can be modeled systems with weighted components. In this paper, we study the mean instantaneous performance of this type of systems after successive component failures. The mean instantaneous performance is a useful characteristic to take preventive action about the system. In particular, we obtain explicit expressions for the mean instantaneous performance of a system with weighted components that have arbitrarily distributed lifetimes. We illustrate the results when the lifetime distribution of components follow proportional hazard model. Some further results are also presented for the components having exponential lifetime distribution. (C) 2013 Elsevier Ltd. All rights reserved.Article Citation - WoS: 11Citation - Scopus: 12A New Mixed Δ-Shock Model With a Change in Shock Distribution(Springer, 2023) Chadjiconstantinidis, Stathis; Tuncel, Altan; Eryilmaz, SerkanIn this paper, reliability properties of a system that is subject to a sequence of shocks are investigated under a particular new change point model. According to the model, a change in the distribution of the shock magnitudes occurs upon the occurrence of a shock that is above a certain critical level. The system fails when the time between successive shocks is less than a given threshold, or the magnitude of a single shock is above a critical threshold. The survival function of the system is studied under both cases when the times between shocks follow discrete distribution and when the times between shocks follow continuous distribution. Matrix-based expressions are obtained for matrix-geometric discrete intershock times and for matrix-exponential continuous intershock times, as well.Article Citation - WoS: 5Citation - Scopus: 6Parallel and Consecutive-k-out-of-n< Systems Under Stochastic Deterioration(Elsevier Science inc, 2014) Eryilmaz, SerkanIn this paper, we study parallel and consecutive-k-out-of-n:F systems consisting of components which are subject to random deterioration with time. The random deterioration in resistance of a component is defined through a stochastic process. We obtain lifetime distribution of a parallel system via classical probabilistic techniques. The lifetime distribution of a consecutive-k-out-of-n:F system is derived using the lifetime distribution of parallel systems and the concept of maximal signature. We also study the optimal replacement time for a parallel system. We present illustrative computational results using MATHCAD. (C) 2013 Elsevier Inc. All rights reserved.Article Citation - WoS: 20Citation - Scopus: 20(k1< k2< km< System and Its Reliability(Elsevier Science Bv, 2019) Eryilmaz, SerkanThis paper is concerned with a system consisting of multiple types of components and having (k(1), k(2),..., k(m))-out-of-n structure. The (k(1), k(2),.., k(m))-out-of-n system is a system consisting of n components of type i, i = 1, 2,..., m, and functions if at least k(1) components of type 1, k(2) components of type 2,..., k(m) components of type m work, n = Sigma(n)(i=1) n(i). The exact and approximate expressions are obtained for the survival function of the system under concern. The weighted-(k(1), k(2),..., k(m))-out-of-n system is also defined and studied. This weighted model is applied to evaluate the wind power system that consists of two wind plants. (C) 2018 Elsevier B.V. All rights reserved.Article Citation - WoS: 1Citation - Scopus: 2On the First Time of Ruin in Two-Dimensional Discrete Time Risk Model With Dependent Claim Occurrences(Taylor & Francis inc, 2018) Eryilmaz, SerkanThis article is concerned with a two-dimensional discrete time risk model based on exchangeable dependent claim occurrences. In particular, we obtain a recursive expression for the finite time non ruin probability under such a dependence among claim occurrences. For an illustration, we define a bivariate compound beta-binomial risk model and present numerical results on this model by comparing the corresponding results of the bivariate compound binomial risk model.Article Citation - WoS: 29Citation - Scopus: 31Computing Marginal and Joint Birnbaum, and Barlow-Proschan Importances in Weighted-k-out-of-n< Systems(Pergamon-elsevier Science Ltd, 2014) Eryilmaz, Serkan; Bozbulut, Ali RizaA weighted-k-out-of-n:G system is a system that consists of n binary components, each with its own positive weight, and operates only when the total weight of working components is at least k. Such a structure is useful when the components have different contributions to the performance of the entire system. This paper is concerned with both marginal and joint Birnbaum, and Barlow-Proschan (BP) importances of the components in weighted- k-out-of-n:G systems. The method of universal generating function is used for computing marginal and joint Birnbaum importances. The method for computing BP-importance is based on a direct probabilistic approach. Extensive numerical calculations are presented. By the help of these calculations and illustrations, it is possible to observe how the marginal and joint importances change with respect to the weights of components. (C) 2014 Elsevier Ltd. All rights reserved.Article Citation - WoS: 5Component Importance in Coherent Systems With Exchangeable Components(Cambridge Univ Press, 2015) Eryilmaz, SerkanThis paper is concerned with the Birnbaum importance measure of a component in a binary coherent system. A representation for the Birnbaum importance of a component is obtained when the system consists of exchangeable dependent components. The results are closely related to the concept of the signature of a coherent system. Some examples are presented to illustrate the results.Article Citation - WoS: 61Citation - 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: 66Citation - Scopus: 76Multivariate 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: 14Citation - Scopus: 14The Number of Failed Components in Series-Parallel System and Its Application To Optimal Design(Pergamon-elsevier Science Ltd, 2020) Eryilmaz, Serkan; Ozkurt, Fatma Yerlikaya; Erkan, T. ErmanThe number of components that are failed at the time of system failure is a useful quantity since it gives an idea of how many spares should be available to replace all failed components upon the system failure. In this paper, the number of failed components is considered at subsystem and system levels for the series-parallel system that consists of K subsystems. In particular, the joint behavior of the number of failed components in each subsystem is studied when each subsystem has identical components and different subsystems have different types of components. The results are then used to find the optimal number of components in each subsystem by minimizing an expected cost per unit of time upon the system failure.
