Computing minimal signature of coherent systems through matrix-geometric distributions. (September 2021)

• Record Type: Journal Article
• Authors: Eryilmaz, Serkan; Tank, Fatih
• Is Part Of: Journal of applied probability. Volume 58:Number 3(2021)
• Page Start: 621
• Page End: 636
• Publication Date: 2021-09
• Subjects: Matrix-geometric distribution -- minimal signature -- probability generating function -- reliability -- signature; 62N05 -- 60K10; 519.2
• DOI: 10.1017/jpr.2021.5
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract: Signatures 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.