11 results
Search Results
Now showing 1 - 10 of 11
Article Citation - WoS: 43Citation - Scopus: 50On the lifetime behavior of a discrete time shock model(Elsevier, 2013) Eryilmaz, SerkanIn this article, we study a shock model in which the shocks occur according to a binomial process, i.e. the interarrival times between successive shocks follow a geometric distribution with mean 1/p. According to the model, the system fails when the time between two consecutive shocks is less than a prespecified level. This is the discrete time version of the so-called delta-shock model which has been previously studied for the continuous case. We obtain the probability mass function and probability generating function of the system's lifetime. We also present an extension of the results to the case where the shock occurrences are dependent in a Markovian fashion. (C) 2012 Elsevier B.V. All rights reserved.Article Citation - WoS: 6Citation - Scopus: 7Modeling 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: 61Citation - Scopus: 72Generalized δ-shock model via runs(Elsevier Science Bv, 2012) Eryilmaz, SerkanAccording to the delta-shock model, the system fails when the time between two consecutive shocks falls below a fixed threshold delta. This model has a potential application in various fields such as inventory, insurance and system reliability. In this paper, we study run-related generalization of this model such that the system fails when k consecutive interarrival times are less than a threshold delta. The survival function and the mean value of the failure time of the system are explicitly derived for exponentially distributed interarrival times. We also propose a new combined shock model which considers both the magnitudes of successive shocks and the interarrival times. (C) 2011 Elsevier B.V. All rights reserved.Article Citation - WoS: 60Citation - Scopus: 64Computing Optimal Replacement Time and Mean Residual Life in Reliability Shock Models(Pergamon-elsevier Science Ltd, 2017) Eryilmaz, SerkanIn this paper, matrix-based methods are presented to compute the optimal replacement time and mean residual lifetime of a system under particular class of reliability shock models. The times between successive shocks are assumed to have a common continuous phase-type distribution. The system's lifetime is represented as a compound random variable and some properties of phase-type distributions are utilized. Extreme shock model, run shock model, and generalized extreme shock model are shown to be the members of this class. Graphical illustrations and numerical examples are presented for the run shock model when the interarrival times between shocks follow Erlang distribution. (C) 2016 Elsevier Ltd. All rights reserved.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: 9Citation - Scopus: 10Reliability 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: 20Citation - Scopus: 23A New Generalized Δ-Shock Model and Its Application To 1-out-of-(m+1):g Cold Standby System(Elsevier Sci Ltd, 2023) Eryilmaz, Serkan; Unlu, Kamil DemirberkAccording to the classical delta-shock model, the system failure occurs upon the occurrence of a new shock that arrives in a time length less than delta, a given positive value. In this paper, a new generalized version of the delta-shock model is introduced. Under the proposed model, the system fails if there are m shocks that arrive in a time length less than delta after a previous shock, m >= 1. The mean time to failure of the system is approximated for both discretely and continuously distributed intershock time distributions. The usefulness of the model is also shown to study 1-out-of-(m + 1):G cold standby system. Illustrative numerical results are presented for geometric, exponential, discrete and continuous phase-type intershock time distributions.Article Citation - WoS: 55Citation - Scopus: 59Assessment of a Multi-State System Under a Shock Model(Elsevier Science inc, 2015) Eryilmaz, SerkanA system is subject to random shocks over time. Let c(1) and c(2) be two critical levels such that c(1) < c(2). A shock with a magnitude between c(1) and c(2) has a partial damage on the system, and the system transits into a lower partially working state upon the occurrence of each shock in (c(1), c(2)). A shock with a magnitude above c(2) has a catastrophic affect on the system and it causes a complete failure. Such a shock model creates a multi-state system having random number of states. The lifetime, the time spent by the system in a perfect functioning state, and the total time spent by the system in partially working states are defined and their survival functions are derived when the interarrival times between successive shocks follow phasetype distribution. (C) 2015 Elsevier Inc. All rights reserved.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: 7Citation - Scopus: 6On δ-shock model with a change point in intershock time distribution(Elsevier, 2024) Chadjiconstantinidis, Stathis; Eryilmaz, SerkanIn this paper, we study the reliability of a system that works under o-shock model. That is, the system failure occurs when the time between two successive shocks is less than a given threshold o. In a traditional setup of the o shock model, the intershock times are assumed to have the same distribution. In the present setup, a change occurs in the distribution of the intershock times due to an environmental effect. Thus, the distribution of the intershock times changes after a random number of shocks. The reliability of the system is studied under this change point setup.
