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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: 10Citation - Scopus: 10Systems Composed of Two Types of Nonidentical and Dependent Components(Wiley-blackwell, 2015) Eryilmaz, Serkan; Eryılmaz, Serkan; Eryılmaz, Serkan; Industrial Engineering; Industrial EngineeringA coherent system of order n that consists two different types of dependent components is considered. The lifetimes of the components in each group are assumed to follow an exchangeable joint distribution, and the two random vectors, which represent the lifetimes of the components in each group are also assumed to be dependent. Under this particular form of dependence, all components are assumed to be dependent but they are categorized with respect to their reliability functions. Mixture representation is obtained for the survival function of the system's lifetime. Mixture representations are also obtained for the series and parallel systems consisting of disjoint modules such that all components of Type I are involved in one module (subsystem) and all components of Type II are placed in the other module. The theoretical results are illustrated with examples. (c) 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 388-394, 2015
