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Article Citation - WoS: 65Citation - Scopus: 75Multivariate 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: 1Citation - Scopus: 2On Bivariate Compound Sums(Elsevier, 2020) Tank, Fatih; Eryilmaz, SerkanThe study of compound sums have always been very popular in the literature. Many models in insurance and engineering have been represented and solved by compound sums. In this paper, two different bivariate compound sums are proposed and studied. The phase-type distribution is applied to obtain the probability generating function of the bivariate sum. (C) 2019 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: 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: 11Citation - Scopus: 10Modeling of Claim Exceedances Over Random Thresholds for Related Insurance Portfolios(Elsevier, 2011) Eryilmaz, Serkan; Gebizlioglu, Omer L.; Tank, FatihLarge claims in an actuarial risk process are of special importance for the actuarial decision making about several issues like pricing of risks, determination of retention treaties and capital requirements for solvency. This paper presents a model about claim occurrences in an insurance portfolio that exceed the largest claim of another portfolio providing the same sort of insurance coverages. Two cases are taken into consideration: independent and identically distributed claims and exchangeable dependent claims in each of the portfolios. Copulas are used to model the dependence situations. Several theorems and examples are presented for the distributional properties and expected values of the critical quantities under concern. (C) 2011 Elsevier B.V. All rights reserved.Article Citation - WoS: 20Citation - Scopus: 20On Optimal Age Replacement Policy for a Class of Coherent Systems(Elsevier, 2020) Eryilmaz, Serkan; Eryılmaz, Serkan; Pekalp, Mustafa Hilmi; Eryılmaz, Serkan; Industrial Engineering; Industrial EngineeringAccording to the well-known age replacement policy, the system is replaced preventively at time t or correctively at system failure, whichever occurs first. For a coherent system consisting of components having common failure time distribution which has increasing failure rate, we present necessary conditions for the existence of the unique optimal value which minimizes the mean cost rate. The conditions are mainly based on the signature which only depends on the system's structure. The results are illustrated for linear and circular consecutive type systems. (C) 2020 Elsevier B.V. All rights reserved.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: 43Citation - Scopus: 50On the lifetime behavior of a discrete time shock model(Elsevier, 2013) Eryilmaz, SerkanIn this article, we study a shock model in which the shocks occur according to a binomial process, i.e. the interarrival times between successive shocks follow a geometric distribution with mean 1/p. According to the model, the system fails when the time between two consecutive shocks is less than a prespecified level. This is the discrete time version of the so-called delta-shock model which has been previously studied for the continuous case. We obtain the probability mass function and probability generating function of the system's lifetime. We also present an extension of the results to the case where the shock occurrences are dependent in a Markovian fashion. (C) 2012 Elsevier B.V. All rights reserved.Article Citation - WoS: 56Citation - Scopus: 58Reliability Analysis Under Marshall-Olkin Run Shock Model(Elsevier, 2019) Ozkut, Murat; Eryilmaz, SerkanIn this paper, a new shock model called Marshall-Olkin run shock model is defined and studied. According to the model, two components are subject to shocks that may arrive from three different sources, and component i fails when it is subject to k consecutive critical shocks from source i or k consecutive critical shocks from source 3, i = 1, 2. Reliability and mean residual life functions of such components are studied when the times between shocks follow phase-type distribution. (C) 2018 Elsevier B.V. All rights reserved.Article Citation - WoS: 1Citation - Scopus: 1Estimation of Parameters for a System Equipped with Protection Block(Elsevier, 2026) Kus, Colkun; Eryilmaz, SerkanThis paper studies the problem of estimating unknown parameters involved in a system which is equipped with a protection block. The system has different failure rates depending on whether the protection block is present or not, as the protection block is modeled by its own lifetime distribution and contributes an additional failure component to the system. The model is analyzed under the assumption of exponentially distributed lifetimes, leading to the study of its distributional properties and the estimation problem for its unknown parameters. Closed-form expressions for the maximum likelihood estimators are obtained. Furthermore, theoretical expectations and variances of the estimators are derived. We also discuss the stress-strength reliability estimation problem and construct confidence intervals for the associated reliability measure. Numerical results are provided to demonstrate the implementation of the proposed methods.
