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Article Citation - WoS: 28Citation - Scopus: 33System Reliability Under Δ-Shock Model(Taylor & Francis inc, 2018) Tuncel, Altan; Eryilmaz, Serkandelta-shock model is one of the widely studied shock models in reliability. Under this model, the system fails when the time between two consecutive shocks falls below a fixed threshold . In this paper, the survival function and the mean time to failure of the system are obtained when the times between successive shocks follow proportional hazard rate model.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: 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: 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: 11Citation - Scopus: 12A New Mixed Δ-Shock Model With a Change in Shock Distribution(Springer, 2023) Chadjiconstantinidis, Stathis; Tuncel, Altan; Eryilmaz, SerkanIn this paper, reliability properties of a system that is subject to a sequence of shocks are investigated under a particular new change point model. According to the model, a change in the distribution of the shock magnitudes occurs upon the occurrence of a shock that is above a certain critical level. The system fails when the time between successive shocks is less than a given threshold, or the magnitude of a single shock is above a critical threshold. The survival function of the system is studied under both cases when the times between shocks follow discrete distribution and when the times between shocks follow continuous distribution. Matrix-based expressions are obtained for matrix-geometric discrete intershock times and for matrix-exponential continuous intershock times, as well.Article Citation - WoS: 13Citation - Scopus: 13Reliability Assessment of a Discrete Time Cold Standby Repairable System(Springer, 2021) Kan, Cihangir; Eryilmaz, SerkanThis paper is concerned with the study of a discrete time repairable system consisting of one active and one standby component. The lifetime and repair time are assumed to have discrete phase-type distributions. The system's lifetime is represented as a compound random variable. A matrix-based expression for the probability generating function of the system's lifetime is obtained based on the phase characteristics of lifetime and repair time distributions. The probability generating function is then used to obtain the distribution of the system's lifetime. Reliability and hazard rate functions are computed and evaluated for some particular choices of lifetime and repair time distributions. The limiting behavior of the hazard rates is also investigated.Article Citation - WoS: 19Citation - Scopus: 14Assessment 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.Article Citation - WoS: 4Citation - Scopus: 4Relative Behavior of a Coherent System With Respect To Another Coherent System(Springer, 2015) Eryilmaz, Serkan; Tutuncu, G. YazgiIn this paper, two independent coherent systems with different structures, and different types of components are considered. The remaining lifetime and the remaining number of working components of system I after the failure of the system II when we know that the system II fails before the system I are studied. In particular, signature-based expressions are obtained for the distribution of these conditional random variables. Illustrative examples are provided.Article Citation - WoS: 6Citation - Scopus: 6Reliability Assessment for Censored Δ-Shock Models(Springer, 2022) Chadjiconstantinidis, Stathis; Eryilmaz, SerkanThis paper is devoted to study censored delta-shock models for both cases when the intershock times have discrete and continuous distributions. In particular, the distribution and moments of the system's lifetime are studied via probability generating functions and Laplace transforms. For discrete intershock time distributions, several recursions for evaluating the probability mass function, the survival function and the moments of the system's lifetime are given. As it is shown for the discrete case, the distribution of the system's lifetime is directly linked with matrix-geometric distributions for particular classes of intershock time distributions, such as phase-type distributions. Thus, matrix-based expressions are readily obtained for the exact distribution of the system's lifetime under discrete setup. Also, discrete uniform intershock time distributions are examined. For the case of continuous intershock time distributions, it is shown that the shifted lifetime has a compound geometric distribution, and based on this, the distribution of the system's lifetime is approximated via discrete mixture distributions having a mass at delta and matrix-exponential distributions for the continuous part. Both for the discrete and the continuous case, Lundberg-type bounds and asymptotics for the survival function of system's lifetime are given. To illustrate the results, some numerical examples, both for the discrete and the continuous case, are also given.Article Citation - WoS: 6Citation - Scopus: 6On Reliability of Consecutive k-out-of-n:G System Equipped With Protection Blocks(Taylor & Francis Ltd, 2026) Eryilmaz, SerkanThe linear consecutive k-out-of-n:G system consists of n linearly ordered components such that the system works properly when there exists at least k consecutively working components. This paper is concerned with the reliability evaluation of the linear consecutive k-out-of-n: G system equipped with protection blocks. Protection blocks which have their failure rates are used to increase the system reliability. The closed-form expressions for the system reliability when $ 2k\geq n $ 2k >= n are obtained when the most critical components, i.e. the components that have the highest importance levels are involved by the protection blocks. Numerical examples are provided to illustrate the closed-form reliability equations.
