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Article Citation - WoS: 12Citation - Scopus: 15Dynamic Reliability Evaluation of Consecutive-K System(Taylor & Francis inc, 2011) Eryilmaz, Serkan; Kan, CihangirA consecutive k-within-m-out-of-n:F system consists of n linearly ordered components and fails if and only if there are m consecutive components which include among them at least k failed components. This system model generalizes both consecutive k-out-of-n:F and k-out-of-n:F systems. In this article, we study the dynamic reliability properties of consecutive k-within-m-out-of-n:F system consisting of exchangeable dependent components. We also obtain some stochastic ordering results and use them to get simple approximation formulae for the survival function and mean time to failure of this system.Article Citation - WoS: 22Citation - Scopus: 23On Residual Lifetime of Coherent Systems After the rth Failure(Springer, 2013) Eryilmaz, SerkanIn this article we study the residual lifetime of a coherent system after the rth failure, i.e. the time elapsed from the rth failure until the system failure given that the system operates at the time of the rth failure. We provide a mixture representation for the corresponding residual lifetime distribution in terms of signature. We also obtain some stochastic ordering results for the residual lifetimes.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: 17Citation - Scopus: 16A Study on Reliability of Coherent Systems Equipped With a Cold Standby Component(Springer Heidelberg, 2014) Eryilmaz, SerkanIn this paper, we investigate the effect of a single cold standby component on the performance of a coherent system. In particular, we focus on coherent systems which may fail at the time of the first component failure in the system. We obtain signature based expressions for the survival function and mean time to failure of the coherent systems satisfying the abovementioned property.Article Citation - WoS: 9Citation - Scopus: 12The Behavior of Warm Standby Components With Respect To a Coherent System(Elsevier Science Bv, 2011) Eryilmaz, SerkanThis paper is concerned with a coherent system consisting of active components and equipped with warm standby components. In particular, we study the random quantity which denotes the number of surviving warm standby components at the time of system failure. We represent the distribution of the corresponding random variable in terms of system signature and discuss its potential utilization with a certain optimization problem. (C) 2011 Elsevier B.V. All rights reserved.Article Citation - WoS: 4Citation - Scopus: 4Relative Behavior of a Coherent System With Respect To Another Coherent System(Springer, 2015) Eryilmaz, Serkan; Tutuncu, G. YazgiIn this paper, two independent coherent systems with different structures, and different types of components are considered. The remaining lifetime and the remaining number of working components of system I after the failure of the system II when we know that the system II fails before the system I are studied. In particular, signature-based expressions are obtained for the distribution of these conditional random variables. Illustrative examples are provided.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: 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: 12Citation - Scopus: 14On Signatures of Series and Parallel Systems Consisting of Modules With Arbitrary Structures(Taylor & Francis inc, 2014) Eryilmaz, SerkanThe signature of a system is a useful concept not only in the analysis of binary coherent systems but also in network reliability. Computation of system signature is a well-defined combinatorial problem. This article is concerned with the computation of signature vectors of series and parallel systems consisting of modules. We derive simple formulas for the signature and minimal signature of series and parallel systems based on signatures and minimal signatures of modules with given structures. We present computational results to illustrate the findings.Article Citation - WoS: 18Citation - Scopus: 21Failure Rates of Consecutive k-out-of-n< Systems(Springer Heidelberg, 2012) Eryilmaz, Serkan; Navarro, JorgeLinear and circular consecutive k-out-of-n systems are very popular models in reliability theory, survival analysis, and biological disciplines and other related lifetime sciences. In these theories, the failure rate function is a key notion for measuring the ageing process. In this paper we obtain some mixture representations for consecutive systems and we apply a mixture-based failure rate analysis for both linear and circular consecutive systems. In particular, we analyze the limiting behavior of the system failure rate when the time increases and we obtain some ordering properties. We first consider the popular case of systems with components having independent and identically distributed lifetimes. In practice, these assumptions may fail. So we also study the case of independent non-identically distributed component lifetimes. This case has special interest when a cold-standby redundancy is used for some components. In this sense, we analyze where to place the best components in the systems. Even more, we also study systems with dependent components by assuming that their lifetimes are exchangeable. (C) 2011 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.
