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Article Citation - WoS: 14Citation - Scopus: 15Dynamic Modeling of General Three-State k-out-of-n< Systems: Permanent-Based Computational Results(Elsevier Science Bv, 2014) Eryilmaz, Serkan; Xie, MinThis paper is concerned with dynamic reliability analysis of three-state k-out-of-n:G systems. It is assumed that the components and the systems can be in three states: perfect functioning, partial performance and complete failure. Using the concept of permanent, we study marginal and joint survival functions for the lifetime of two different three-state k-out-of-n:G systems that consist of independent and nonidentical components. Illustrative examples are also provided for the components which follow the Markov degradation process. (C) 2014 Elsevier B.V. All rights reserved.Article Citation - WoS: 5Citation - Scopus: 5On the Sums of Distributions of Order Statistics From Exchangeable Random Variables(Elsevier Science Bv, 2013) Eryilmaz, SerkanIn this paper, we obtain an expression between the sums of the marginal distributions of the order statistics and the common marginal distribution of an exchangeable random sequence. We also derive an expression between the sums of the joint distribution of two order statistics and the two dimensional joint distribution of an exchangeable random sequence. (C) 2013 Elsevier B.V. All rights reserved.Article Citation - WoS: 20Citation - Scopus: 28Reliability Analysis of Consecutive k-out-of-n< Systems With Non-Identical Components Lifetimes(Elsevier Science Bv, 2011) Salehi, E. T.; Asadi, M.; Eryilmaz, S.In recent years, the study of reliability properties of consecutive k-out-of-n systems has attracted a great deal of attention from both theoretical and practical perspectives. In this paper we consider linear and circular consecutive k-out-of-n systems. It is assumed that lifetimes of components of the systems are independent but their probability distributions are non-identical. We study the reliability properties of the residual lifetimes of such systems under the condition that at least (n - r + 1), r <= n, components of the system are operating. We also investigate the probability that a specific number of components of the above-mentioned system operate at time t, t > 0, under the condition that the system is alive at time t. (C) 2011 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: 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 - 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: 53Citation - Scopus: 60On the Mean Residual Life of a k-out-of-n< System With a Single Cold Standby Component(Elsevier Science Bv, 2012) Eryilmaz, SerkanThe concept of mean residual life is one of the most important characteristics that has been widely used in dynamic reliability analysis. It is a useful tool for investigating ageing properties of technical systems. In this paper, we define and study three different mean residual life functions for k-out-of-n:G system with a single cold standby component. In particular, we obtain explicit expressions for the corresponding functions using distributions of order statistics. We also provide some stochastic ordering results associated with the lifetime of a system. We illustrate the results for various lifetime distributions. (c) 2012 Elsevier B.V. All rights reserved.Article Citation - WoS: 44Citation - Scopus: 53On Reliability Analysis of a k-out-of-n< System With Components Having Random Weights(Elsevier Sci Ltd, 2013) Eryilmaz, SerkanConsider a system consisting of n components each with its own positive integer-valued random weight (capacity). The system is assumed to have a performance level above c if there are at least k working components, and the total weight of all working components is above c. We study the reliability properties of such a system. A recursive formula is obtained for computing the system state probabilities. We present a Monte-Carlo simulation algorithm to observe the time spent by the system in state c or above. The algorithm is based on the use of ordered lifetimes of components. We illustrate the results with numerical computations. (C) 2012 Elsevier Ltd. All rights reserved.Article Citation - WoS: 8Citation - Scopus: 12On the Mean Residual Lifetime of Consecutive K-Out Systems(Springer, 2012) Salehi, E. T.; Asadi, M.; Eryilmaz, S.In recent years, consecutive systems were shown to have many applications in various branches of science such as engineering. This paper is a study on the stochastic and aging properties of residual lifetime of consecutive k-out-of-n systems under the condition that n-r+1, ra parts per thousand currency signn, components of the system are working at time t. We consider the linear and circular consecutive k-out-of-n systems and propose a mean residual lifetime (MRL) for such systems. Several properties of the proposed MRL is investigated. The mixture representation of the MRL of the systems with respect to the vector of signatures of the system is also studied.Article Citation - WoS: 6Citation - Scopus: 7Order Statistics of Dependent Sequences Consisting of Two Different Sets of Exchangeable Variables(Elsevier Science Bv, 2015) Bayramoglu (Bairamov), Ismihan; Eryilmaz, SerkanWe consider two different sets of exchangeable samples which are assumed to be dependent. A single set of observations is obtained from these two dependent samples. The distribution of single order statistic, and the joint distribution of the minimum and an arbitrary order statistic are derived. The results are illustrated in the context of reliability problem. (C) 2015 Elsevier B.V. All rights reserved.
