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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.Article Citation - WoS: 22Citation - Scopus: 24Computing reliability indices of repairable systems via signature(Elsevier Science Bv, 2014) Eryilmaz, SerkanThe purpose of this paper is to show the usefulness of system signature for computing some important reliability indices of repairable systems. In particular, we obtain signature-based expressions for stationary availability, rate of occurrence of failure, and mean time to the first failure of repairable systems. Using these expressions we compute corresponding reliability indices of all systems with three and four components. Computational results are also presented for consecutive-k-within-m-out-of-n:F and m-consecutive-k-out-of-n:F systems. (C) 2013 Elsevier B.V. All rights reserved.Article Citation - WoS: 4Citation - Scopus: 4On compound sums under dependence(Elsevier, 2017) Eryilmaz, SerkanIn this paper, we study the compound random variable S = Sigma(N)(t-1) Y-t when there is a dependence between a random variable N and a sequence of random variables {Y-t}(t >= 1). Such a compound random variable has been found to be useful in several fields including actuarial science, risk management, and reliability. In particular, we develop some results on distributional properties of the random variable S when N is a phase-type random variable that is defined on a sequence of binary trials and depends on {Y-t}(t >= 1). We "present illustrative examples and an application for the use of results in actuarial science. (C) 2016 Elsevier B.V. All rights reserved.Article Citation - WoS: 57Citation - Scopus: 61Assessment of a Multi-State System Under a Shock Model(Elsevier Science inc, 2015) Eryilmaz, SerkanA system is subject to random shocks over time. Let c(1) and c(2) be two critical levels such that c(1) < c(2). A shock with a magnitude between c(1) and c(2) has a partial damage on the system, and the system transits into a lower partially working state upon the occurrence of each shock in (c(1), c(2)). A shock with a magnitude above c(2) has a catastrophic affect on the system and it causes a complete failure. Such a shock model creates a multi-state system having random number of states. The lifetime, the time spent by the system in a perfect functioning state, and the total time spent by the system in partially working states are defined and their survival functions are derived when the interarrival times between successive shocks follow phasetype distribution. (C) 2015 Elsevier Inc. All rights reserved.Article Citation - WoS: 44Citation - Scopus: 52The Number of Failed Components in a Coherent System With Exchangeable Components(Ieee-inst Electrical Electronics Engineers inc, 2012) Eryilmaz, SerkanThis paper is concerned with the number of components that are failed at the time of system failure. We study the corresponding quantity for a coherent structure via the system signature. Furthermore, we study the distribution of the number of failures after a specified time until the system failure. We illustrate the results for well-known general classes of coherent systems such as linear consecutive k-within-m-out-of- n:F, and m-consecutive-k-out-of-: n:F.Article Citation - WoS: 24Citation - Scopus: 30Dynamic Assessment of Multi-State Systems Using Phase-Type Modeling(Elsevier Sci Ltd, 2015) Eryilmaz, SerkanMulti-state systems have attracted great attention due to their wide applications in engineering. They have been effectively used in modeling various systems such as power supply systems and transportation systems. In this paper, phase type modeling is proposed for dynamic assessment of nonrepairable multi-state systems when the system degrades According to a Markov process. The utility of phase type modeling is demonstrated in the computation of mean lifetimes, mean residual lifetimes, and derivation of survival functions of series and parallel systems. A stochastic comparison result between two systems is also obtained using phase representations of survival functions. Extensive numerical results are presented to illustrate the applicability of the approach. (C) 2015 Elsevier Ltd. All rights reserved.Article Citation - WoS: 9Citation - Scopus: 9Mixture Representations for Three-State Systems With Three-State Components(Ieee-inst Electrical Electronics Engineers inc, 2015) Eryilmaz, SerkanThis paper is concerned with dynamic reliability modeling of three-state systems consisting of three-state s-independent components. The components and the systems are assumed to be in three states: perfect functioning, partial performance, and complete failure. Survival functions of such systems are studied in different state subsets. It is shown that the survival function of a three-state system with a general structure can be represented as a mixture of the survival functions of the three-state k-out-of-n:G systems. The results are illustrated for the three-state consecutive-k-out-of-n:G systems whose components degrade according to a Markov process.Article Citation - WoS: 11Citation - Scopus: 13Compound Markov Negative Binomial Distribution(Elsevier, 2016) Eryilmaz, SerkanLet {Y-i}(i >= 1) be a sequence of {0,1} variables which forms a Markov chain with a given initial probability distribution and one-step transition probability matrix. Define N-n to be the number of trials until the nth success ("1") in {Y-i}(i >= 1). In this paper, we study the distribution of the random variable T = Sigma(Nn)(i=1) X-i, where {X-i}(i >= 1) is a sequence of independent and identically distributed random variables having a common phase-type distribution. The distribution of T is obtained by means of phase-type distributions. (C) 2015 Elsevier B.V. All rights reserved.
