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Article Citation - WoS: 1Citation - Scopus: 2Computing Minimal Signature of Coherent Systems Through Matrix-Geometric Distributions(Cambridge Univ Press, 2021) Eryilmaz, Serkan; Eryılmaz, Serkan; Tank, Fatih; Eryılmaz, Serkan; Industrial Engineering; Industrial EngineeringSignatures are useful in analyzing and evaluating coherent systems. However, their computation is a challenging problem, especially for complex coherent structures. In most cases the reliability of a binary coherent system can be linked to a tail probability associated with a properly defined waiting time random variable in a sequence of binary trials. In this paper we present a method for computing the minimal signature of a binary coherent system. Our method is based on matrix-geometric distributions. First, a proper matrix-geometric random variable corresponding to the system structure is found. Second, its probability generating function is obtained. Finally, the companion representation for the distribution of matrix-geometric distribution is used to obtain a matrix-based expression for the minimal signature of the coherent system. The results are also extended to a system with two types of components.Article Citation - WoS: 2Citation - Scopus: 2A New Extended δ-shock Model With the Consideration of Shock Magnitude(Wiley, 2024) Lorvand, Hamed; Eryilmaz, SerkanIn this article, a new delta$$ \delta $$-shock model that takes into account the magnitude of shocks is introduced and studied from reliability perspective. According to the new model, the system breaks down if either a shock after non-critical shock occurs in a time length less than delta 1$$ {\delta}_1 $$ or a shock after a critical shock occurs in a time length less than delta 2,$$ {\delta}_2, $$ where delta 1Article 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: 7Citation - Scopus: 9Reliability of the Two-Unit Priority Standby System Revisited(Sage Publications Ltd, 2022) Eryilmaz, Serkan; Finkelstein, MaximThis paper deals with reliability assessment of the repairable two-unit cold standby system when the first, main unit has the better performance level than the second one. Therefore, after its repair, the main unit is always switched into operation. The new Laplace transform representation for the system's lifetime is obtained for arbitrary operation and repair time distributions of the units. For some particular cases, the Laplace transform of the system is shown to be rational, which enables the use of the matrix-exponential distributions for obtaining relevant reliability indices. The discrete setup of the model is also considered through the corresponding matrix-geometric distributions, which are the discrete analogs of the matrix-exponential distributions.
