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Article Citation - WoS: 5Component Importance in Coherent Systems With Exchangeable Components(Cambridge Univ Press, 2015) Eryilmaz, SerkanThis 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.Article Citation - WoS: 38Citation - Scopus: 46Generalizing the Survival Signature To Unrepairable Homogeneous Multi-State Systems(Wiley, 2016) Eryilmaz, Serkan; Tuncel, AltanThe notion of signature has been widely applied for the reliability evaluation of technical systems that consist of binary components. Multi-state system modeling is also widely used for representing real life engineering systems whose components can have different performance levels. In this article, the concept of survival signature is generalized to a certain class of unrepairable homogeneous multi-state systems with multi-state components. With such a generalization, a representation for the survival function of the time spent by a system in a specific state or above is obtained. The findings of the article are illustrated for multi-state consecutive-k-out-of-n system which perform its task at three different performance levels. The generalization of the concept of survival signature to a multi-state system with multiple types of components is also presented. (C) 2016 Wiley Periodicals, Inc.Article Citation - WoS: 4Citation - Scopus: 6On Profust Reliability of Coherent Systems: Signature-Based Expressions(Sage Publications Ltd, 2013) Eryilmaz, Serkan; Rouyendegh, Babak DaneshvarIn this article we study profust reliability of non-repairable coherent systems through the concept of system signature. We obtain explicit expressions for the profust reliability and mean time to fuzzy failure of coherent systems. We compute and present mean time to failure and mean time to fuzzy failure of all coherent systems with three and four components. Finally, we illustrate the results for a well known class of coherent systems called m-consecutive-k-out-of-n:F.Article Citation - WoS: 1Citation - Scopus: 2Computing Minimal Signature of Coherent Systems Through Matrix-Geometric Distributions(Cambridge Univ Press, 2021) Eryilmaz, Serkan; Eryılmaz, Serkan; Tank, Fatih; Eryılmaz, Serkan; Industrial Engineering; Industrial EngineeringSignatures are useful in analyzing and evaluating coherent systems. However, their computation is a challenging problem, especially for complex coherent structures. In most cases the reliability of a binary coherent system can be linked to a tail probability associated with a properly defined waiting time random variable in a sequence of binary trials. In this paper we present a method for computing the minimal signature of a binary coherent system. Our method is based on matrix-geometric distributions. First, a proper matrix-geometric random variable corresponding to the system structure is found. Second, its probability generating function is obtained. Finally, the companion representation for the distribution of matrix-geometric distribution is used to obtain a matrix-based expression for the minimal signature of the coherent system. The results are also extended to a system with two types of components.Article Citation - WoS: 10Citation - Scopus: 10Systems Composed of Two Types of Nonidentical and Dependent Components(Wiley-blackwell, 2015) Eryilmaz, Serkan; Eryılmaz, Serkan; Eryılmaz, Serkan; Industrial Engineering; Industrial EngineeringA coherent system of order n that consists two different types of dependent components is considered. The lifetimes of the components in each group are assumed to follow an exchangeable joint distribution, and the two random vectors, which represent the lifetimes of the components in each group are also assumed to be dependent. Under this particular form of dependence, all components are assumed to be dependent but they are categorized with respect to their reliability functions. Mixture representation is obtained for the survival function of the system's lifetime. Mixture representations are also obtained for the series and parallel systems consisting of disjoint modules such that all components of Type I are involved in one module (subsystem) and all components of Type II are placed in the other module. The theoretical results are illustrated with examples. (c) 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 388-394, 2015Article Citation - WoS: 15Citation - Scopus: 16Residual Lifetime of Consecutive k-out-of-n< Systems Under Double Monitoring(Ieee-inst Electrical Electronics Engineers inc, 2012) Eryilmaz, Serkan; Bayramoglu, KonulThe consecutive k-out-of-n systems are important structures in reliability engineering due to their applications in various real life situations. In this paper, we study the residual lifetime of these systems under the condition that the total number of failed components at time is, and at time t(2) (t(2) > t(1)) the system is still working. We obtain explicit expressions for the survival function of the corresponding residual life when the components are exchangeably dependent. We also obtain a signature-based mixture representation for a coherent system satisfying a certain property.Article Citation - WoS: 18Citation - Scopus: 17Reliability of Combined m-consecutive-k< and Consecutive kc< Systems(Ieee-inst Electrical Electronics Engineers inc, 2012) Eryilmaz, SerkanA combined m-consecutive-k-out-of-n:F & consecutive-k(c)-out-of-n:F system consists of linearly ordered components, and fails iff there exist at least k(c) consecutive failed components, or at least m non-overlapping runs of k consecutive failed components. This structure has applications for modeling systems such as infrared detecting and signal processing, and bank automatic payment systems. In this paper, we derive a combinatorial equation for the number of path sets of this structure including a specified number of working components. This number is used to derive a reliability function, and a signature based survival function formulae, for the system consisting of i.i.d. components. We also obtain a combinatorial equation for the reliability of a system with Markov dependent components.
