53 results
Search Results
Now showing 1 - 10 of 53
Article Citation - WoS: 18Citation - Scopus: 21Modeling Dependence Between Two Multi-State Components Via Copulas(Ieee-inst Electrical Electronics Engineers inc, 2014) Eryilmaz, SerkanModeling statistical dependence between two systems or components is an important problem in reliability theory. Such a problem has been well studied for binary systems and components. In the present paper, we provide a way for modeling s-dependence between two multi-state components. Our method is based on the use of copulas which are very popular for modeling s-dependence. We obtain expressions for the joint state probabilities of the two components, and illustrate the results for the case when the degradation in both components follows a Markov process.Book Citation - Scopus: 15Discrete Stochastic Models and Applications for Reliability Engineering and Statistical Quality Control(CRC Press, 2022) Eryilmaz,S.Discrete stochastic models are tools that allow us to understand, control, and optimize engineering systems and processes. This book provides real-life examples and illustrations of models in reliability engineering and statistical quality control and establishes a connection between the theoretical framework and their engineering applications. The book describes discrete stochastic models along with real-life examples and explores not only well-known models, but also comparatively lesser known ones. It includes definitions, concepts, and methods with a clear understanding of their use in reliability engineering and statistical quality control fields. Also covered are the recent advances and established connections between the theoretical framework of discrete stochastic models and their engineering applications. An ideal reference for researchers in academia and graduate students working in the fields of operations research, reliability engineering, quality control, and probability and statistics. © 2023 Serkan Eryilmaz.Article Citation - WoS: 6Citation - Scopus: 7Parallel and Consecutive-k-out-of-n< Systems Under Stochastic Deterioration(Elsevier Science inc, 2014) Eryilmaz, SerkanIn this paper, we study parallel and consecutive-k-out-of-n:F systems consisting of components which are subject to random deterioration with time. The random deterioration in resistance of a component is defined through a stochastic process. We obtain lifetime distribution of a parallel system via classical probabilistic techniques. The lifetime distribution of a consecutive-k-out-of-n:F system is derived using the lifetime distribution of parallel systems and the concept of maximal signature. We also study the optimal replacement time for a parallel system. We present illustrative computational results using MATHCAD. (C) 2013 Elsevier Inc. All rights reserved.Article Citation - WoS: 20Citation - Scopus: 20(k1< k2< km< System and Its Reliability(Elsevier Science Bv, 2019) Eryilmaz, SerkanThis paper is concerned with a system consisting of multiple types of components and having (k(1), k(2),..., k(m))-out-of-n structure. The (k(1), k(2),.., k(m))-out-of-n system is a system consisting of n components of type i, i = 1, 2,..., m, and functions if at least k(1) components of type 1, k(2) components of type 2,..., k(m) components of type m work, n = Sigma(n)(i=1) n(i). The exact and approximate expressions are obtained for the survival function of the system under concern. The weighted-(k(1), k(2),..., k(m))-out-of-n system is also defined and studied. This weighted model is applied to evaluate the wind power system that consists of two wind plants. (C) 2018 Elsevier B.V. All rights reserved.Article Citation - WoS: 1Citation - Scopus: 2On the First Time of Ruin in Two-Dimensional Discrete Time Risk Model With Dependent Claim Occurrences(Taylor & Francis inc, 2018) Eryilmaz, SerkanThis article is concerned with a two-dimensional discrete time risk model based on exchangeable dependent claim occurrences. In particular, we obtain a recursive expression for the finite time non ruin probability under such a dependence among claim occurrences. For an illustration, we define a bivariate compound beta-binomial risk model and present numerical results on this model by comparing the corresponding results of the bivariate compound binomial risk model.Article Citation - WoS: 25Citation - Scopus: 28Lifetime of Multistate k-out-of-n< Systems(Wiley-blackwell, 2014) Eryilmaz, SerkanA multistate k-out-of-n system model is an extension of binary k-out-of-n system model by allowing multiple performance levels for the system and its components. Various definitions of multistate k-out-of-n system model have been proposed in the literature. Previous studies on these systems mostly focus on reliability evaluation algorithms. The present paper investigates the lifetimes of multistate systems. In particular, the lifetimes of two different multistate k-out-of-n system models are represented in terms of order statistics, and bounds and approximations are presented using these representations. The results are illustrated for a multistate system whose components' degradation occurs according to a Markov process. Copyright (C) 2013 John Wiley & Sons, Ltd.Article Citation - WoS: 67Citation - Scopus: 79Multivariate Copula Based Dynamic Reliability Modeling With Application To Weighted-k-out-of-n< Systems of Dependent Components(Elsevier, 2014) Eryilmaz, SerkanIn this paper, a multivariate copula based modeling methodology for dynamic reliability modeling of weighted-k-out-of-n systems is applied. The system under consideration is assumed to have n dependent components each having its own weight. It has a performance level of at least k when the total weight of operating components is k or above. Copula based expressions for the survival function and mean time to failure of such a system are obtained. Extensive numerical results are presented for Clayton and Gumbel type copulas. The behavior of survival function and mean time to failure are investigated with respect to the value of Kendall's correlation coefficient. (C) 2014 Elsevier Ltd. All rights reserved.Article Citation - WoS: 11Citation - Scopus: 12Reliability 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: 22Citation - Scopus: 24Computing reliability indices of repairable systems via signature(Elsevier Science Bv, 2014) Eryilmaz, SerkanThe purpose of this paper is to show the usefulness of system signature for computing some important reliability indices of repairable systems. In particular, we obtain signature-based expressions for stationary availability, rate of occurrence of failure, and mean time to the first failure of repairable systems. Using these expressions we compute corresponding reliability indices of all systems with three and four components. Computational results are also presented for consecutive-k-within-m-out-of-n:F and m-consecutive-k-out-of-n:F systems. (C) 2013 Elsevier B.V. All rights reserved.Article Citation - WoS: 7Citation - Scopus: 8A new look at dynamic behavior of binary coherent system from a state-level perspective(Springer, 2014) Eryilmaz, SerkanIn this paper we study lifetime properties of binary coherent systems from a state-level perspective. We define and study a system whose performance levels are determined by its total number of working components and structure. That is, the more working components the better performance level for the system. This enables us to make a more detailed analysis of a binary system. We obtain the distributions of the time that is spent by the system in a specific state subset and a specific state. Our analysis is based on the use of system signature. We also define an optimization problem concerned with the determination of the number of warm standby components.
