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Article Citation - WoS: 3Citation - Scopus: 3On the Mean Number of Remaining Components in Three-State k-out-of-n< System(Elsevier Science Bv, 2015) Eryilmaz, Serkan; Eryılmaz, Serkan; Eryılmaz, Serkan; Industrial Engineering; Industrial EngineeringA three-state k-out-of-n system with n independent components is considered, where the vector k of integers is determined by given fixed scalars k(1) and k(2) such that k(1), k(2) <= n. The mean number of components of each type either in a perfect functioning state or in a partially working state at the time of the system failure and at a time while the system is working are studied. An optimization problem concerned with the most economical value of n is also formulated. (C) 2015 Elsevier B.V. All rights reserved.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.
