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Article Citation - Scopus: 5Component Importance in Coherent Systems With Exchangeable Components(Applied Probability Trust, 2015) Eryilmaz,S.This 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. © 2015 Applied Probability Trust.Article Citation - WoS: 14Citation - Scopus: 16Joint Reliability Importance in Coherent Systems With Exchangeable Dependent Components(Ieee-inst Electrical Electronics Engineers inc, 2016) Eryilmaz, Serkan; Oruc, Ozlem Ege; Oger, VolkanIn this paper, a general formula for computing the joint reliability importance of two components is obtained for a binary coherent system that consists of exchangeable dependent components. Using the new formula, the joint reliability importance can be easily calculated if the path sets of the system are known. As a special case, an expression for the joint reliability importance of two components is also obtained for a system consisting of independent and identical components. Illustrative numerical results are presented to compare the joint reliability importance of two components in the bridge system for the two cases when the components are exchangeable dependent and when the components are independent and identical.Article Citation - WoS: 21Citation - Scopus: 29On Reliability Analysis of a Two-Dependent Series System With a Standby Unit(Elsevier Science inc, 2012) Eryilmaz, Serkan; Tank, FatihIn this paper we study a series system with two active components and a single cold standby unit. The two simultaneously working components are assumed to be dependent and this dependence is modeled by a copula function. In particular, we obtain an explicit expression for the mean time to failure of the system in terms of the copula function and marginal lifetime distributions. We also provide illustrative numerical results for different copula functions and marginal lifetime distributions. (c) 2012 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: 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: 5Citation - Scopus: 5Some Reliability Measures and Maintenance Policies for a Coherent System Composed of Different Types of Components(Springer Heidelberg, 2023) Kelkinnama, Maryam; Eryilmaz, SerkanConsider an n-components coherent system monitored at one or two inspection times, and some information about the system and its components is obtained. Under these conditions, some variants of mean residual lifetimes can be defined. Also, the dual concept of the residual lifetime, i.e., inactivity time is defined for a failed system under different conditions. This article is concerned with the study of mean residual lives and mean inactivity times for a coherent system made of multiple types of dependent components. The dependency structure is modeled by a survival copula. The notion of survival signature is employed to represent the system's reliability function and subsequently its mean residual lives and mean inactivity times under different events at the monitoring time. These dynamic measures are used frequently to study the reliability characteristics of a system. Also, they provide helpful tools for designing the optimal maintenance policies to preserving the system from sudden and costly failures. Here, we extend some maintenance strategies for a coherent system consists of multiple dependent components. Some illustrative examples are provided.Article Citation - WoS: 8Citation - Scopus: 13Joint Reliability Importance in a Binary k-out-of- n: G System With Exchangeable Dependent Components(Nctu-national Chiao Tung Univ Press, 2014) Mahmoud, Boushaba; Eryilmaz, SerkanIn this paper, we study joint reliability importance (JRI) in a k -out-of- n : G structure consisting of exchangeable dependent coimponents. We obtain a closed-form formula for the JRI of multiple components of a k -out-of- n : G system with dependent components. We illustrate the results for the k -out-of- n: G model under stress-strength setup. The results extend and generalize the results in the literature from various perspectives including exchangeable type dependence for the JRI of two components.Article Citation - WoS: 5Citation - Scopus: 6Computing Finite Time Non-Ruin Probability and Some Joint Distributions in Discrete Time Risk Model With Exchangeable Claim Occurrences(Elsevier, 2017) Eryilmaz, Serkan; Gebizlioglu, Omer L.In this paper, we study a discrete time risk model based on exchangeable dependent claim occurrences. In particular, we obtain expressions for the finite time non-ruin probability, and the joint distribution of the time to ruin, the surplus immediately before ruin, and the deficit at ruin. An illustration of the results is given and some implications of the results are provided. Comparisons are made with the corresponding results for the classical compound binomial model of independent and identically distributed claim occurrences. (C) 2016 Elsevier E.V. All rights reserved.Article Citation - WoS: 27Citation - Scopus: 27Joint Reliability Importance in Linear m-consecutive-k< F Systems(Ieee-inst Electrical Electronics Engineers inc, 2013) Eryilmaz, SerkanWe study the joint reliability importance (JRI) of two components in Lin/m/Con/k/n : F systems. A Lin/m/Con/k/n : F system consists of n linearly ordered binary components, and the system fails iff there are at least m nonoverlapping runs of k consecutive failed components (n >= mk). In particular, we obtain expressions for the JRI in Lin/m/Con/k/n : F systems when the components are s-independent & identical, when the components are s-independent & nonidentical, and when the components are exchangeable & s-dependent. We present extensive numerical illustrations.Article Citation - WoS: 9Citation - Scopus: 13The Concept of Weak Exchangeability and Its Applications(Springer Heidelberg, 2017) Eryilmaz, SerkanA finite sequence of binary random variables is called a weak exchangeable sequence of order m if the sequence consists of m random vectors such that the elements within each random vector are exchangeable in the usual sense and the different random vectors are dependent. The exact and asymptotic joint distributions of the m-dimensional random vector whose elements include the number of successes in each exchangeable sequence are derived. Potential applications of the concept of weak exchangeability are discussed with illustrative examples.
