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Article Citation - WoS: 23Citation - Scopus: 26Lifetime of Multistate k-out-of-n< Systems(Wiley-blackwell, 2014) Eryilmaz, SerkanA multistate k-out-of-n system model is an extension of binary k-out-of-n system model by allowing multiple performance levels for the system and its components. Various definitions of multistate k-out-of-n system model have been proposed in the literature. Previous studies on these systems mostly focus on reliability evaluation algorithms. The present paper investigates the lifetimes of multistate systems. In particular, the lifetimes of two different multistate k-out-of-n system models are represented in terms of order statistics, and bounds and approximations are presented using these representations. The results are illustrated for a multistate system whose components' degradation occurs according to a Markov process. Copyright (C) 2013 John Wiley & Sons, Ltd.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: 9Citation - Scopus: 9Mixture Representations for Three-State Systems With Three-State Components(Ieee-inst Electrical Electronics Engineers inc, 2015) Eryilmaz, SerkanThis paper is concerned with dynamic reliability modeling of three-state systems consisting of three-state s-independent components. The components and the systems are assumed to be in three states: perfect functioning, partial performance, and complete failure. Survival functions of such systems are studied in different state subsets. It is shown that the survival function of a three-state system with a general structure can be represented as a mixture of the survival functions of the three-state k-out-of-n:G systems. The results are illustrated for the three-state consecutive-k-out-of-n:G systems whose components degrade according to a Markov process.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: 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: 59Citation - Scopus: 68Reliability of a k-out-of-n< System Equipped With a Single Warm Standby Component(Ieee-inst Electrical Electronics Engineers inc, 2013) Eryilmaz, SerkanAk - out - of - n : system consists of components, and operates if at least of its components operate. Its reliability properties have been widely studied in the literature from different perspectives. This paper is concerned with the reliability analysis of a k - out - of - n : G system equipped with a single warm standby unit. We obtain an explicit expression for the reliability function of the system for arbitrary lifetime distributions. Two different mean residual life functions are also studied for the system.Article Citation - WoS: 44Citation - Scopus: 52Signature Based Analysis of m-consecutive-k< f Systems With Exchangeable Components(Wiley-blackwell, 2011) Eryilmaz, Serkan; Koutras, Markos V.; Triantafyllou, Ioannis S.In this article, we study reliability properties of m-consecutive-k-out-of-n: F systems with exchangeable components. We deduce exact formulae and recurrence relations for the signature of the system. Closed form expressions for the survival function and the lifetime distribution as a mixture of the distribution of order statistics are established as well. These representations facilitate the computation of several reliability characteristics of the system for a given exchangeable joint distribution or survival function. Finally, we provide signature-based stochastic ordering results for the system's lifetime and investigate the IFR preservation property under the formulation of m-consecutive-k-out-of-n: F systems. (C) 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 344-354, 2011Article Citation - WoS: 17Citation - Scopus: 21Computing the Signature of a Generalized k-out-of-n< System(Ieee-inst Electrical Electronics Engineers inc, 2015) Eryilmaz, Serkan; Tuncel, AltanA generalized k-out-of-n system which is denoted by ((n(1), ... , n(N)), f, k) consists N of modules ordered in a line or a circle, and the ith module is composed of n(i) components in parallel. (n(i) >= 1, i = 1, ... , N). The system fails iff there exist at least failed components or at least k consecutive failed modules. In this paper, we compute the signature of this system when n(1) = ... = n(N) = n, and present illustrative examples to demonstrate its application. Simulation based computation of the signature is provided when the modules have different numbers of components.
