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Article Citation - WoS: 27Citation - Scopus: 30The Distributions of Sum, Minima and Maxima of Generalized Geometric Random Variables(Springer, 2015) Tank, Fatih; Eryilmaz, SerkanGeometric distribution of order as one of the generalization of well known geometric distribution is the distribution of the number of trials until the first consecutive successes in Bernoulli trials with success probability . In this paper, it is shown that this generalized distribution can be represented as a discrete phase-type distribution. Using this representation along with closure properties of phase-type distributions, the distributions of sum, minima and maxima of two independent random variables having geometric distribution of order are obtained. Numerical results are presented to illustrate the computational details.Article Citation - WoS: 77Citation - Scopus: 80Reliability and Optimal Replacement Policy for an Extreme Shock Model With a Change Point(Elsevier Sci Ltd, 2019) Eryilmaz, Serkan; Kan, CihangirAn extreme shock model when there is a change in the distribution of the magnitudes of shocks is defined and studied. Such a model is useful in practice since a sudden change in environmental conditions may cause a larger shock. In particular, the reliability and mean time to failure of the system is obtained by assuming that the times between arrivals of shocks follow phase-type distribution. The optimal replacement policy that is based on a control limit is also proposed. The results are illustrated when the number of shocks until the change point follows geometric distribution.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: 11Citation - Scopus: 11Reliability and Performance Evaluation of Weighted K-out-of- N :g System Consisting of Components With Discrete Lifetimes(Elsevier Sci Ltd, 2024) Eryilmaz, SerkanFor the k-out-of-n n system consisting of components that have different weights, the system is in a good state if the total weight of working components is at least k . Such a system is known to be weighted k-out-of- n :G system. Although the weighted k-out-of-n n system that has continuously distributed components' lifetimes has been extensively studied, the discrete weighted k-out-of- n :G system has not been considered yet. The present paper fills this gap by modeling and analyzing the weighted k-out-of-n:G n :G system that consists of discretely distributed components' lifetimes. In particular, the behavior of the total capacity/weight of the system with respect to the component failures is evaluated. An optimization problem that is concerned with the determination of optimal number of spare components is also formulated by utilizing the mean lost capacity of the system.Article Citation - WoS: 36Citation - Scopus: 42Modeling and Analysis of Weighted-k-out-of-n< G System Consisting of Two Different Types of Components(Sage Publications Ltd, 2014) Eryilmaz, Serkan; Sarikaya, KadirThis article is concerned with the reliability analysis of a weighted-k-out-of-n: G system consisting of two types of components. The system is assumed to have n components which are classified into two groups with respect to their weight and reliability, and it is assumed to operate if the total weight of all working components exceeds a prespecified threshold k. The reliability properties of such a system are studied. The optimal values of the number of components in each group are also determined under a minimum required reliability by minimizing the total acquisition cost.Article Citation - WoS: 2Citation - Scopus: 1Age replacement policies for discrete and continuous heterogeneous k-out-of-n systems(Springer, 2024) Eryilmaz, Serkan; Bulanik, IremThis paper studies age replacement policy for the k-out-of-n system that consists of independent but nonidentical components. Both continuously and discretely distributed components' lifetimes are considered. The failed components are replaced by new components and non-failed components are rejuvenated. Because the components are non-identical, the acquisition and rejuvenation costs of the components are chosen differently. The policy and the associated optimization problem are presented for general k and n, and 2-out-of-3 systems are studied in detail. The findings of the present paper extend the results in the literature from parallel systems to k-out-of-n systems.Article Citation - WoS: 6Citation - Scopus: 6Discrete Time Cold Standby Repairable System: Combinatorial Analysis(Taylor & Francis inc, 2016) Eryilmaz, SerkanIn this article, we obtain exact expression for the distribution of the time to failure of discrete time cold standby repairable system under the classical assumptions that both working time and repair time of components are geometric. Our method is based on alternative representation of lifetime as a waiting time random variable on a binary sequence, and combinatorial arguments. Such an exact expression for the time to failure distribution is new in the literature. Furthermore, we obtain the probability generating function and the first two moments of the lifetime random variable.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: 14Citation - Scopus: 16Reliability of Linear Wsns: a Complementary Overview and Analysis of Impact of Cascaded Failures on Network Lifetime(Elsevier, 2022) Carsancakli, Muhammed Fatih; Imran, Md Abdullah Al; Yildiz, Huseyin Ugur; Kara, Ali; Tavli, BulentLinear Wireless Sensor Networks (LWSNs) are used in applications where deployment scenarios necessitate sensor nodes to be placed over a line topology. However, such a deployment raises reliability concerns because almost all the nodes in the network are critical with respect to the survivability of the LWSN. It is possible that an LWSN can stay connected even if a subset of the nodes are eliminated, yet, the potential reduction in Network Lifetime (NL) due to such an occurrence can be significant. In this study, after presenting a concise survey of the literature on LWSN reliability, we present an elaborate optimization framework to model the operation of an LWSN, which is built upon a comprehensive system model. Our framework encompasses three transmission power and packet size assignment strategies, which are instrumental in characterizing LWSN behavior. Furthermore, we utilized two-node failure models (i.e., random and coordinated) to assess the vulnerability of LWSNs from multiple perspectives. The results of this study reveal that the impact of coordinated node failures on NL is more severe than the impact of random node failures to such extent that in strongly connected LWSNs, the percentage decrease in NL due to coordinated node failures can be more than a magnitude higher than the NL decrease due to random node failures.Article Citation - WoS: 20Citation - Scopus: 15Assessment of Shock Models for a Particular Class of Intershock Time Distributions(Springer, 2022) Kus, Coskun; Tuncel, Altan; Eryilmaz, SerkanIn this paper, delta and extreme shock models and a mixed shock model which combines delta-shock and extreme shock models are studied. In particular, the interarrival times between successive shocks are assumed to belong to a class of matrix-exponential distributions which is larger than the class of phase-type distributions. The Laplace -Stieltjes transforms of the systems' lifetimes are obtained in a matrix form. Survival functions of the systems are approximated based on the Laplace-Stieltjes transforms. The results are applied for the reliability evaluation of a certain repairable system consisting of two components.
