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Article Citation - WoS: 6Citation - Scopus: 6Some 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.Doctoral Thesis Füze Sistemlerinin Güvenilirlik Tahmini için Yeni Bir Yaklaşım(2012) Genç, Yiğit Koray; Güray, Cenk; Arıkan, Kutluk BilgeGünümüzde güvenilirlik bir mühendislik sisteminin en önemli performans göstergelerinden biri haline gelmiştir. Son yıllarda, problemlerin karmaşıklığı arttığından, bu problemleri ele alacak mühendislik sistemlerinin de karmaşıklığı artmaktadır. Buna göre sistemleri oluşturan bileşen sayılarında artış görülmektedir. Belirtilen her iki etken de maliyet artışına sebep olmakta ve ağırlık, boyut vb. kısıtlamalar çerçevesinde daha rekabetçi ürünler ortaya koymayı gerektirmektedir. Savunma sanayi güvenilirlik çalışmalarının sıkça kullanıldığı bir alandır. Bu alanda füze, uçak, helikopter, tank sistemleri gibi son derece karmaşık ve pahalı sistemler yer almaktadır. Zorlu operasyon koşullarında kendilerine atanan kritik görevleri yerine getirmek için tasarlanan bu sistemlerin dayanıklılık ve performans gereksinimleri, bu sistemlerin daha güvenilir tasarlanabilmeleri için güvenilirlik tahmini yapılmasına olanak sağlayacak araçlar gerektirmektedir. Bu tezde, füze sistemlerinin henüz tasarım aşamasında iken güvenilirliğini tahmin etmeyi sağlayacak ve karar destek sistemi olarak kullanılabilecek yeni bir bulanık tahmin yöntemi önerilmektedir.Article Citation - WoS: 6Citation - Scopus: 6Estimating the Parameter of a Geometric Distribution From Series System Data(Elsevier, 2024) Eryilmaz, Serkan; Kateri, MariaIn a traditional setup of estimation of an unknown parameter of component lifetime distribution, system's continuous lifetime data is used. In this paper, we propose a simple and competitive estimator that is based on discrete lifetime data, i.e., the number of failed components at the time when the system fails. In particular, we consider the estimation of the parameter of a geometric distribution based on the system's lifetime data, and the number of failed components upon the failure of the system when the system has a series structure. Two moment estimators that are based on the system lifetime data and the number of failed components at the moment of system failure are obtained and their performances are compared in terms of the mean square error. The associated Bayesian estimators with non -informative priors are also discussed.Article Citation - WoS: 25Citation - Scopus: 33Dynamic Behavior of k-out-of-n< Systems(Elsevier, 2011) Eryilmaz, Serkan; Erylmaz, SerkanIn this paper, we study the distribution and expected value of the number of working components at time t in usual and weighted k-out-of-n:G systems under the condition that they are working at time t. We evaluate the distribution of the corresponding conditional random variable and compute its expected value for the systems consisting of independent but nonidentical components. Illustrative examples are presented and an optimization problem which makes use of the conditional random variable is also formulated and solved numerically. (c) 2011 Elsevier B.V. All rights reserved.Article Citation - WoS: 10Citation - Scopus: 10Reliability and Optimal Age-Based Replacement Policy for Consecutive 2-Out System Equipped With Protection Blocks(Pergamon-Elsevier Science Ltd, 2025) Eryilmaz, SerkanThis paper concerns the reliability evaluation and optimal age-based replacement policy for the linear consecutive 2-out-of-n:G system whose two consecutive components are protected by a block that has its own failure rate. Two alternative methods are proposed to compute the reliability of the system. The first method is based on direct probabilistic approach and uses the reliability of the ordinary consecutive 2-outof-n:G system. The second method is based on the concept of survival signature. Closed form equations for the system reliability and the mean number of failed components within the system are obtained. The optimal age-based replacement policy is also defined and studied. Extensive numerical results are presented to illustrate the findings.Article Citation - WoS: 16Citation - Scopus: 17Dynamic 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 A General Type of Linear Consecutive-K Systems(Springer, 2026) Yi, He; Balakrishnan, Narayanaswamy; Li, XiangIn this paper, some well-known consecutive k-type systems, including linear consecutive-k-out-of-n: F systems and linear l-consecutive-k-out-of-n: F systems without/with overlapping, are generalized by using more general failure patterns. Finite Markov chain imbedding approach (FMCIA) is applied in a new way for evaluating reliabilities of these generalized new systems. Some illustrative examples are provided for demonstrating the theoretical results established here and also for showing the efficiency of the computational process. Finally, some possible applications and generalizations are mentioned.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.Article Citation - WoS: 8Citation - Scopus: 8On 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.Article Citation - WoS: 66Citation - Scopus: 78Multivariate 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.
