15 results
Search Results
Now showing 1 - 10 of 15
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: 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: 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.Article Citation - WoS: 12Citation - Scopus: 15Dynamic Reliability Evaluation of Consecutive-K System(Taylor & Francis inc, 2011) Eryilmaz, Serkan; Kan, CihangirA consecutive k-within-m-out-of-n:F system consists of n linearly ordered components and fails if and only if there are m consecutive components which include among them at least k failed components. This system model generalizes both consecutive k-out-of-n:F and k-out-of-n:F systems. In this article, we study the dynamic reliability properties of consecutive k-within-m-out-of-n:F system consisting of exchangeable dependent components. We also obtain some stochastic ordering results and use them to get simple approximation formulae for the survival function and mean time to failure of this system.Article Citation - WoS: 6Citation - Scopus: 7Modeling 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: 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: 4Citation - Scopus: 2A New Class of Bivariate Lifetime Distributions(Taylor & Francis inc, 2017) Eryilmaz, SerkanThis paper introduces a new class of bivariate lifetime distributions. Let {X-i}(i 1) and {Y-i}(i 1) be two independent sequences of independent and identically distributed positive valued random variables. Define T-1 = min(X-1, ..., X-M) and T-2 = min(Y-1, ..., Y-N), where (M, N) has a discrete bivariate phase-type distribution, independent of {X-i}(i 1) and {Y-i}(i 1). The joint survival function of (T-1, T-2) is studied.Article Citation - WoS: 12Citation - Scopus: 14On Signatures of Series and Parallel Systems Consisting of Modules With Arbitrary Structures(Taylor & Francis inc, 2014) Eryilmaz, SerkanThe signature of a system is a useful concept not only in the analysis of binary coherent systems but also in network reliability. Computation of system signature is a well-defined combinatorial problem. This article is concerned with the computation of signature vectors of series and parallel systems consisting of modules. We derive simple formulas for the signature and minimal signature of series and parallel systems based on signatures and minimal signatures of modules with given structures. We present computational results to illustrate the findings.Article Citation - WoS: 12Citation - Scopus: 18Phase Type Stress-Strength Models With Reliability Applications(Taylor & Francis inc, 2018) Eryilmaz, SerkanThe stress-strength model has attracted a great deal of attention in reliability analysis, and it has been studied under various modeling assumptions. In this article, the stress-strength reliability is studied for both single unit and multicomponent systems when stress and strength distributions are of phase type. Phase-type distributions, besides their analytical tractability, are a versatile tool for modeling a wide range of real life systems/processes. In particular, matrix-based expressions are obtained for the stress-strength reliability, and mean residual strength for an operating system. The results are illustrated for Erlang-type stress-strength distributions for a single unit system and a system having a general coherent structure. An example on the comparison of two multi-state units in stress-strength ordering is also presented.
