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Article Citation - Scopus: 5Component Importance in Coherent Systems With Exchangeable Components(Applied Probability Trust, 2015) Eryilmaz,S.This paper is concerned with the Birnbaum importance measure of a component in a binary coherent system. A representation for the Birnbaum importance of a component is obtained when the system consists of exchangeable dependent components. The results are closely related to the concept of the signature of a coherent system. Some examples are presented to illustrate the results. © 2015 Applied Probability Trust.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 - Scopus: 28On stress-strength reliability with a time-dependent strength(John Wiley and Sons Ltd, 2013) Eryilmaz,S.The study of stress-strength reliability in a time-dependent context needs to model at least one of the stress or strength quantities as dynamic. We study the stress-strength reliability for the case in which the strength of the system is decreasing in time and the stress remains fixed over time; that is, the strength of the system is modeled as a stochastic process and the stress is considered to be a usual random variable. We present stochastic ordering results among the lifetimes of the systems which have the same strength but are subjected to different stresses. Multicomponent form of the aforementioned stress-strength interference is also considered. We illustrate the results for the special case when the strength is modeled by a Weibull process. © 2013 Serkan Eryilmaz.Article Citation - Scopus: 22M-Consecutive System With Overlapping Runs: Signature-Based Reliability Analysis(Inderscience Publishers, 2012) Eryilmaz,S.Consecutive-k-out-of-n system and its generalisations have attracted substantial interest due to their applications to model telecommunications systems, oil pipeline systems, heating systems, etc. One of the most important generalisation of this system is an m-consecutive-k-out-of-n:F system. An m-consecutive-k-out-of-n:F system with overlapping runs is a system consisting of n linearly ordered components and fails if and only if there are at least m overlapping runs of k consecutive failures. For m = 1, the system is same with the usual consecutive-k-out-of-n:F system. In this paper, we study the reliability properties of such systems via system signature. In particular, we obtain a closed form expression for the signature of this system and use it to compute and evaluate several reliability characteristics of the system. Copyright © 2012 Inderscience Enterprises Ltd.Article Citation - WoS: 9Citation - Scopus: 11Start-up demonstration tests under Markov dependence(Isoss Publ, 2010) Eryilmaz,S.A start-up demonstration test is a mechanism that can be used to demonstrate the reliability of an equipment to the customer. In this paper, we study CSTF (consecutive successes total failures) and TSTF (total successes total failures) procedures assuming that the individual start-ups follow a first order Markov dependence structure. Explicit (nonrecursive) expressions for the distributions of the test lengths are provided. Maximum likelihood and moments estimators of the expected test length are obtained and some numerical results are presented for an illustration. © 2010 Pakistan Journal of Statistics.
