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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.Article Citation - WoS: 35Citation - Scopus: 43Reliability Analysis of Multi-State System With Three-State Components and Its Application To Wind Energy(Elsevier Sci Ltd, 2018) Eryilmaz, SerkanIn most real life situations, the system's components contribute differently in different performance levels. Such a situation can be modeled by systems with multi-state components having more than one working status, e.g. perfect functioning, and partial working. In this paper, a multi-state system that consists of two types of three-state components is defined and studied. An explicit formula for the probability that the performance of the system is at least a given level is obtained for the most general case when the components are statistically dependent. The model is applied to evaluate the wind power system that consists of two wind plants in different regions. An optimization problem is formulated to find the optimal number of wind turbines that must be installed in the wind plants by minimizing the total cost under specific power production. (C) 2017 Elsevier Ltd. All rights reserved.Article Citation - WoS: 8Citation - Scopus: 11Joint Distribution of Run Statistics in Partially Exchangeable Processes(Elsevier Science Bv, 2011) Eryilmaz, SerkanLet {X-i}(i >= 1) be an infinite sequence of recurrent partially exchangeable random variables with two possible outcomes as either "1" (success) or "0" (failure). In this paper we obtain the joint distribution of success and failure run statistics in {X-i}(i >= 1). The results can be used to obtain the joint distribution of runs in ordinary Markov chains, exchangeable and independent sequences. (C) 2010 Elsevier B.V. All rights reserved.Article Citation - WoS: 7Citation - Scopus: 8A new look at dynamic behavior of binary coherent system from a state-level perspective(Springer, 2014) Eryilmaz, SerkanIn this paper we study lifetime properties of binary coherent systems from a state-level perspective. We define and study a system whose performance levels are determined by its total number of working components and structure. That is, the more working components the better performance level for the system. This enables us to make a more detailed analysis of a binary system. We obtain the distributions of the time that is spent by the system in a specific state subset and a specific state. Our analysis is based on the use of system signature. We also define an optimization problem concerned with the determination of the number of warm standby components.Article Citation - WoS: 66Citation - Scopus: 78Multivariate 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: 12Reliability 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: 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.
