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Article Citation - WoS: 1A Class of Shock Models for a System That Is Equipped With a Protection Block With an Application to Wind Turbine Reliability(Wiley, 2025) Eryilmaz, SerkanThis paper studies a class of shock models for a system that is equipped with a protection block that has its own failure rate. Under the considered class, the system exposed to shocks at random times is protected by the protection block, and the probability of the shock damaging the system varies depending on whether the protection block operates or not. The system failure criteria is defined based on the pattern of the critical/damaging shocks. Exact expressions for the reliability and mean time to failure of the system are obtained, and detailed computations are presented for the run shock model, which is included in the class. The application of the extreme shock model, which is included in the relevant class, to wind turbine reliability is also discussed.Article Citation - WoS: 1Citation - Scopus: 2On the Lifetime of a Random Binary Sequence(Elsevier Science Bv, 2011) Eryilmaz, SerkanConsider a system with m elements which is used to fulfill tasks. Each task is sent to one element which fulfills a task and the outcome is either fulfillment of the task ("1") or the failure of the element ("0"). Initially, m tasks are sent to the system. At the second step, a complex of length m(1) is formed and sent to the system, where m(1) is the number of tasks fulfilled at the first step, and so on. The process continues until all elements fail and the corresponding waiting time defines the lifetime of the binary sequence which consists of "1" or "0". We obtain a recursive equation for the expected value of this waiting time random variable. (C) 2011 Elsevier B.V. All rights reserved.Article Citation - WoS: 7Citation - Scopus: 7A Generalized Class of Correlated Run Shock Models(de Gruyter Poland Sp Zoo, 2018) Yalcin, Femin; Eryilmaz, Serkan; Bozbulut, Ali RizaIn this paper, a generalized class of run shock models associated with a bivariate sequence {(X-i, Y-i)}(i >= 1) of correlated random variables is defined and studied. For a system that is subject to shocks of random magnitudes X-1, X-2, ... over time, let the random variables Y-1, Y-2, ... denote times between arrivals of successive shocks. The lifetime of the system under this class is defined through a compound random variable T = Sigma(N)(t=1) Y-t, where N is a stopping time for the sequence {Xi}(i >= 1) and represents the number of shocks that causes failure of the system. Another random variable of interest is the maximum shock size up to N, i.e. M = max {X-i, 1 <= i <= N}Distributions of T and M are investigated when N has a phase-type distribution.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: 7Citation - Scopus: 8Modeling Systems With Two Dependent Components Under Bivariate Shock Models(Taylor & Francis inc, 2019) Eryilmaz, SerkanSeries and parallel systems consisting of two dependent components are studied under bivariate shock models. The random variables N-1 and N-2 that represent respectively the number of shocks until failure of component 1 and component 2 are assumed to be dependent and phase-type. The times between successive shocks are assumed to follow a continuous phase-type distribution, and survival functions and mean time to failure values of series and parallel systems are obtained in matrix forms. An upper bound for the joint survival function of the components is also provided under the particular case when the times between shocks follow exponential distribution.Article Citation - WoS: 6Citation - Scopus: 6Dynamic Reliability and Performance Evaluation of Multi-State Systems With Two Components(Hacettepe Univ, Fac Sci, 2011) Eryilmaz, Serkan; Industrial EngineeringIn this paper we study multi-state systems consisting of two components when the number of system states and the number of states of each component are the same, i.e. the systems under consideration are homogeneous multi-state systems. In particular we evaluate multi-state series and cold standby systems assuming that the degradation in their components follow a Markov process. The behaviour of systems with respect to degradation rates is also investigated in terms of stochastic ordering.Editorial Discussion of Signature-Based Models of Preventive Maintenance(Wiley, 2023) Eryilmaz, Serkan[No Abstract Available]Article Citation - WoS: 12Citation - Scopus: 14The Markov Discrete Time Δ-Shock Reliability Model and a Waiting Time Problem(Wiley, 2022) Chadjiconstantinidis, Stathis; Eryilmaz, Serkandelta-shock model is one of the widely studied shock models in reliability theory and applied probability. In this model, the system fails due to the arrivals of two consecutive shocks which are too close to each other. That is, the system breaks down when the time between two successive shocks falls below a fixed threshold delta. In the literature, the delta-shock model has been mostly studied by assuming that the time between shocks have continuous distribution. In the present paper, the discrete time version of the model is considered. In particular, a proper waiting time random variable is defined based on a sequence of two-state Markov dependent binary trials and the problem of finding the distribution of the system's lifetime is linked with the distribution of the waiting time random variable, and we study the joint as well as the marginal distributions of the lifetime, the number of shocks and the number of failures associated with these binary trials.Article Citation - WoS: 26Citation - Scopus: 28Reliability Assessment for Discrete Time Shock Models Via Phase-Type Distributions(Wiley, 2021) Eryilmaz, Serkan; Kan, CihangirIn this paper, particular shock models are studied for the case when the times between successive shocks and the magnitudes of shocks have discrete phase-type distributions. The well-known shock models such as delta shock model, extreme shock model, and the mixed shock model which is obtained by combining delta and extreme shock models are considered. The probability generating function and recursive equation for the distribution of the system's lifetime are obtained for the cases when the interarrival times between shocks and the magnitudes of shocks are independent and when they are dependent. System reliability is computed for particular interarrival distributions such as geometric, negative Binomial and generalized geometric distributions.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.
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