Eryilmaz, SerkanEryılmaz, SerkanTank, FatihEryılmaz, SerkanIndustrial EngineeringIndustrial EngineeringIndustrial Engineering2024-07-052024-07-0520210021-90021475-607210.1017/jpr.2021.52-s2.0-85115313867https://doi.org/10.1017/jpr.2021.5https://hdl.handle.net/20.500.14411/1707Tank, Fatih/0000-0003-3758-396X; Eryilmaz, Serkan/0000-0002-2108-1781Signatures 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.eninfo:eu-repo/semantics/closedAccessMatrix-geometric distributionminimal signatureprobability generating functionreliabilitysignatureArticleQ3583621636WOS:0006963080000061