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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: 11Citation - Scopus: 11Reliability of Systems With Multiple Types of Dependent Components(Ieee-inst Electrical Electronics Engineers inc, 2016) Eryilmaz, SerkanMost practical systems consist of multiple types of components although the components perform the same task within the system. The analysis of such systems is more challenging than the systems with single type of components. In this paper, we present expressions for the survival function of the failure time, and mean time to failure of the system under the general case when the random failure times of components of the same type are exchangeable dependent and the random failure times of components of different type are dependent. As a case study, we apply our results to linear consecutive-k-out-of-n: F systems consisting of three different types of dependent components.Article Citation - WoS: 8Citation - Scopus: 9Mixed Three-State K-Out Systems With Components Entering at Different Performance Levels(Ieee-inst Electrical Electronics Engineers inc, 2016) Eryilmaz, Serkan; Koutras, Markos V.; Triantafyllou, Ioannis S.In this paper, we study a three-state k-out-of-n system with n independent components (k = (k(1), k(2))). Each component can be in a perfect functioning state (state "2"), partially working (state "1"), or failed (state "0"). We assume that, at time t = 0, n(1) components are in a partially working state while the rest n(2) components are fully functioning (n = n(1) + n(2)). The system is considered to be at state "1" or above if at least k(1) components are working (fully or partially). If at least k(1) components are working and at least k(2) components are in a perfect functioning state, we shall say that the system is at state "2". In this paper, we develop formulae for the survival functions corresponding to the two different system's states described above. For illustration purposes, a numerical example which assumes that the degradation occurs according to a Markov process is presented.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.Article Citation - WoS: 23Citation - Scopus: 25Linear m-Consecutive-k, l-Out-of-n: F System(Ieee-inst Electrical Electronics Engineers inc, 2012) Eryilmaz, Serkan; Mahmoud, BoushabaWe propose a new model which generalizes the linear m-consecutive-k-out-of-n: F system to the case of the m-consecutive-k-out-of-n: F system with l-overlapping runs. The new system is called the m-consecutive-k,l-out-of-n: F system, and consists of n linearly ordered components such that the system fails iff there are at least m l-overlapping runs of k consecutive failed components. The number of path sets including a specified number of working components is obtained via a combinatorial method, and this quantity is used to obtain the reliability and the signature of the system.
