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Article Citation - WoS: 56Citation - Scopus: 58Reliability Analysis Under Marshall-Olkin Run Shock Model(Elsevier, 2019) Ozkut, Murat; Eryilmaz, SerkanIn this paper, a new shock model called Marshall-Olkin run shock model is defined and studied. According to the model, two components are subject to shocks that may arrive from three different sources, and component i fails when it is subject to k consecutive critical shocks from source i or k consecutive critical shocks from source 3, i = 1, 2. Reliability and mean residual life functions of such components are studied when the times between shocks follow phase-type distribution. (C) 2018 Elsevier B.V. All rights reserved.Article Citation - WoS: 5Citation - Scopus: 5Some Reliability Measures and Maintenance Policies for a Coherent System Composed of Different Types of Components(Springer Heidelberg, 2023) Kelkinnama, Maryam; Eryilmaz, SerkanConsider an n-components coherent system monitored at one or two inspection times, and some information about the system and its components is obtained. Under these conditions, some variants of mean residual lifetimes can be defined. Also, the dual concept of the residual lifetime, i.e., inactivity time is defined for a failed system under different conditions. This article is concerned with the study of mean residual lives and mean inactivity times for a coherent system made of multiple types of dependent components. The dependency structure is modeled by a survival copula. The notion of survival signature is employed to represent the system's reliability function and subsequently its mean residual lives and mean inactivity times under different events at the monitoring time. These dynamic measures are used frequently to study the reliability characteristics of a system. Also, they provide helpful tools for designing the optimal maintenance policies to preserving the system from sudden and costly failures. Here, we extend some maintenance strategies for a coherent system consists of multiple dependent components. Some illustrative examples are provided.Article Citation - WoS: 21Citation - Scopus: 24Optimization Problems for a Parallel System With Multiple Types of Dependent Components(Elsevier Sci Ltd, 2020) Eryilmaz, Serkan; Ozkut, MuratThis paper is concerned with two optimization problems for a parallel system that consists of dependent components. First, the problem of finding the number of elements in the system that minimizes the mean cost rate of the system is considered. The second problem is concerned with the optimal replacement time of the system. Previous work assumes that the components are independent. We discuss the impact of dropping this assumption. In particular, we numerically examine how the dependence between the components affects the optimal number of units and replacement time for the system which minimize mean cost rates. We first consider the case when the components are exchangeable and dependent, i.e. the system consists of single type of dependent components. Subsequently, we consider a system that consists of multiple types of dependent components. Comparative numerical results are presented for particularly chosen dependence models.Book Part Discrete Scan Statistics Generated by Dependent Trials and Their Applications in Reliability(Springer New York, 2024) Eryilmaz,S.; Yalcin,F.The chapter is concerned with discrete scan statistic based on a sequence of dependent binary trials. In particular, the existing results are reviewed for the distribution of the discrete scan statistic based on a sequence of exchangeable binary trials. The results are discussed in the context of the reliability of the linear consecutive-k-within-m-out-of-n:F system, and a new exact formula for the reliability of the linear consecutive-2-within-m-out-of-n:F system that consists of arbitrarily dependent components is presented. © Springer Science+Business Media, LLC, part of Springer Nature 2024.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: 5Citation - Scopus: 6Parallel 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: 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: 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: 14Citation - Scopus: 15Dynamic Modeling of General Three-State k-out-of-n< Systems: Permanent-Based Computational Results(Elsevier Science Bv, 2014) Eryilmaz, Serkan; Xie, MinThis paper is concerned with dynamic reliability analysis of three-state k-out-of-n:G systems. It is assumed that the components and the systems can be in three states: perfect functioning, partial performance and complete failure. Using the concept of permanent, we study marginal and joint survival functions for the lifetime of two different three-state k-out-of-n:G systems that consist of independent and nonidentical components. Illustrative examples are also provided for the components which follow the Markov degradation process. (C) 2014 Elsevier B.V. All rights reserved.Article Nonparametric Tests for Comparing Reliabilities of Coherent Systems at Specific Mission Time(IEEE-Inst Electrical Electronics Engineers Inc, 2026) Xu, Xuan; Zhu, Xiaojun; Balakrishnan, Narayanaswamy; Ng, Hon Keung TonyReliability analysis of coherent systems is critical for evaluating the performance of systems whose functionality depends on the reliability of their components. Traditional parametric methods for comparing reliabilities of coherent systems assume a specific probability distribution for component lifetimes, which may result in inaccurate results when these model assumptions are violated. This article introduces nonparametric procedures using system-level data with known signatures to compare the reliabilities of systems. The proposed methodology avoids parametric distributional assumptions for component lifetimes while relying on the standard assumption in signature-based reliability analysis. Specifically, a two-sample likelihood ratio test procedure is proposed to demonstrate a component or system with superior reliability. Monte Carlo simulations are performed to evaluate the performance of the proposed methods. Furthermore, we examine the effect of system structure on test power and determine favourable structures to enhance the power performance of the test. Practical examples are used to illustrate the proposed test procedures.
