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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: 6Citation - Scopus: 6Discrete Time Cold Standby Repairable System: Combinatorial Analysis(Taylor & Francis inc, 2016) Eryilmaz, SerkanIn this article, we obtain exact expression for the distribution of the time to failure of discrete time cold standby repairable system under the classical assumptions that both working time and repair time of components are geometric. Our method is based on alternative representation of lifetime as a waiting time random variable on a binary sequence, and combinatorial arguments. Such an exact expression for the time to failure distribution is new in the literature. Furthermore, we obtain the probability generating function and the first two moments of the lifetime random variable.Article Citation - WoS: 7Citation - Scopus: 8Modeling 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: 5Citation - Scopus: 8Reliability Properties of Systems With Two Exchangeable Log-Logistic Components(Taylor & Francis inc, 2012) Eryilmaz, SerkanIn this article, we study the reliability properties of systems under bivariate log-logistic model which comes out from a particular stress-strength analysis. For this model, we obtain basic reliability characteristics of series and parallel systems and investigate their properties. We also derive distribution and moments of cold standby system under the above mentioned exchangeable model.Article Citation - WoS: 4Citation - Scopus: 6Statistical Inference for a Class of Startup Demonstration Tests(Taylor & Francis inc, 2019) Eryilmaz, SerkanIn this article, we develop a general statistical inference procedure for the probability of successful startup p in the case of startup demonstration tests when only the number of trials until termination of the experiment are observed. In particular, we define a class of startup demonstration tests and present expectation-maximization (EM) algorithm to get the maximum likelihood estimate of p for this class. Most of well-known startup testing procedures are involved in this class. Extension of the results to Markovian startups is also presented.Article Citation - WoS: 12Citation - Scopus: 11On an Application of Concomitants of Order Statistics(Taylor & Francis inc, 2016) Eryilmaz, SerkanLet (X-i, Y-i), i = 1, ..., n be a pair where the first coordinate X-i represents the lifetime of a component, and the second coordinate Y-i denotes the utility of the component during its lifetime. Then the random variable Y-[r: n] which is known to be the concomitant of the rth order statistic defines the utility of the component which has the rth smallest lifetime. In this paper, we present a dynamic analysis for an n component system under the above-mentioned concomitant setup.Article Citation - WoS: 34Citation - Scopus: 30Reliability Evaluation for a Multi-State System Under Stress-Strength Setup(Taylor & Francis inc, 2011) Eryilmaz, Serkan; Iscioglu, FundaThe two most commonly used reliability models in engineering applications are binary k-out-of-n:G and consecutive k-out-of-n:G systems. Multi-state k-out-of-n:G and multi-state consecutive k-out-of-n:G systems have been proposed as an extension of these systems and they have been found to be more flexible tool for modeling engineering systems. In this article, multi-state systems, in particular, multi-state k-out-of-n:G and multi-state consecutive k-out-of-n:G, are considered in a stress-strength setup. The states of the system are classified considering the number of components whose strengths above (below) the multiple stresses available in an environment. The exact state probabilities are provided and the results are illustrated for various stress-strength distributions. Maximum likelihood estimators of state probabilities are also presented.Article Citation - WoS: 6Citation - Scopus: 6Reliability Analysis of Systems With Components Having Two Dependent Subcomponents(Taylor & Francis inc, 2017) Eryilmaz, SerkanIn this article, a system that consists of n independent components each having two dependent subcomponents (A(i), B-i), i = 1, ... ,n is considered. The system is assumed to compose of components that have two correlated subcomponents (A(i), B-i), and functions iff both systems of subcomponents A(1),A(2), ... ,A(n) and B-1, B-2, ... , B-n work under certain structural rules. The expressions for reiiabiiity and mean time to failure of such systems are obtained. A sufficient condition to compare two systems of bivariate components in terms of stochastic ordering is also ordering presented.Article Citation - WoS: 29Citation - Scopus: 34System 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: 27Citation - Scopus: 31Generalized Extreme Shock Models and Their Applications(Taylor & Francis inc, 2020) Bozbulut, Ali Riza; Eryilmaz, SerkanIn the classical extreme shock model, the system fails due to a single catastrophic shock. In this paper, by assuming different arrival patterns of the shocks, two new types of extreme shock models are introduced. In these models, m possible sources may exert shocks on the system. Both models reduce to the classical extreme shock model when m = 1. Assuming phase-type distribution for times between successive shocks, we obtain survival functions and mean time to failure values of the system under new models. Two different optimization problems are also considered to determine the optimal number of sources.
