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Article Citation - WoS: 26Citation - Scopus: 28Reliability Assessment for Discrete Time Shock Models Via Phase-Type Distributions(Wiley, 2021) Eryilmaz, Serkan; Kan, CihangirIn this paper, particular shock models are studied for the case when the times between successive shocks and the magnitudes of shocks have discrete phase-type distributions. The well-known shock models such as delta shock model, extreme shock model, and the mixed shock model which is obtained by combining delta and extreme shock models are considered. The probability generating function and recursive equation for the distribution of the system's lifetime are obtained for the cases when the interarrival times between shocks and the magnitudes of shocks are independent and when they are dependent. System reliability is computed for particular interarrival distributions such as geometric, negative Binomial and generalized geometric distributions.Article Citation - WoS: 12Citation - Scopus: 13A NEW SHOCK MODEL WITH A CHANGE IN SHOCK SIZE DISTRIBUTION(Cambridge Univ Press, 2021) Eryilmaz, Serkan; Kan, CihangirFor a system that is subject to shocks, it is assumed that the distribution of the magnitudes of shocks changes after the first shock of size at least d(1), and the system fails upon the occurrence of the first shock above a critical level d(2) (> d(1)). In this paper, the distribution of the lifetime of such a system is studied when the times between successive shocks follow matrix-exponential distribution. In particular, it is shown that the system's lifetime has matrix-exponential distribution when the intershock times follow Erlang distribution. The model is extended to the case when the system fails upon the occurrence of l consecutive critical shocks.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.
