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Article Citation - WoS: 18Citation - Scopus: 21Modeling Dependence Between Two Multi-State Components Via Copulas(Ieee-inst Electrical Electronics Engineers inc, 2014) Eryilmaz, SerkanModeling statistical dependence between two systems or components is an important problem in reliability theory. Such a problem has been well studied for binary systems and components. In the present paper, we provide a way for modeling s-dependence between two multi-state components. Our method is based on the use of copulas which are very popular for modeling s-dependence. We obtain expressions for the joint state probabilities of the two components, and illustrate the results for the case when the degradation in both components follows a Markov process.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, 2013Book Citation - Scopus: 15Discrete Stochastic Models and Applications for Reliability Engineering and Statistical Quality Control(CRC Press, 2022) Eryilmaz,S.Discrete stochastic models are tools that allow us to understand, control, and optimize engineering systems and processes. This book provides real-life examples and illustrations of models in reliability engineering and statistical quality control and establishes a connection between the theoretical framework and their engineering applications. The book describes discrete stochastic models along with real-life examples and explores not only well-known models, but also comparatively lesser known ones. It includes definitions, concepts, and methods with a clear understanding of their use in reliability engineering and statistical quality control fields. Also covered are the recent advances and established connections between the theoretical framework of discrete stochastic models and their engineering applications. An ideal reference for researchers in academia and graduate students working in the fields of operations research, reliability engineering, quality control, and probability and statistics. © 2023 Serkan Eryilmaz.Article Citation - WoS: 66Citation - Scopus: 76Generalized δ-shock model via runs(Elsevier Science Bv, 2012) Eryilmaz, SerkanAccording to the delta-shock model, the system fails when the time between two consecutive shocks falls below a fixed threshold delta. This model has a potential application in various fields such as inventory, insurance and system reliability. In this paper, we study run-related generalization of this model such that the system fails when k consecutive interarrival times are less than a threshold delta. The survival function and the mean value of the failure time of the system are explicitly derived for exponentially distributed interarrival times. We also propose a new combined shock model which considers both the magnitudes of successive shocks and the interarrival times. (C) 2011 Elsevier B.V. All rights reserved.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: 6Citation - 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: 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: 66Citation - Scopus: 77Multivariate 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: 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: 11Citation - Scopus: 11Reliability and Performance Evaluation of Weighted K-out-of- N :g System Consisting of Components With Discrete Lifetimes(Elsevier Sci Ltd, 2024) Eryilmaz, SerkanFor the k-out-of-n n system consisting of components that have different weights, the system is in a good state if the total weight of working components is at least k . Such a system is known to be weighted k-out-of- n :G system. Although the weighted k-out-of-n n system that has continuously distributed components' lifetimes has been extensively studied, the discrete weighted k-out-of- n :G system has not been considered yet. The present paper fills this gap by modeling and analyzing the weighted k-out-of-n:G n :G system that consists of discretely distributed components' lifetimes. In particular, the behavior of the total capacity/weight of the system with respect to the component failures is evaluated. An optimization problem that is concerned with the determination of optimal number of spare components is also formulated by utilizing the mean lost capacity of the system.
