Computing minimal signature of coherent systems through matrix-geometric distributions

Eryilmaz S., Tank F.

JOURNAL OF APPLIED PROBABILITY, vol.58, no.3, pp.621-636, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 58 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.1017/jpr.2021.5
  • Journal Name: JOURNAL OF APPLIED PROBABILITY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Applied Science & Technology Source, CAB Abstracts, INSPEC, MathSciNet, Veterinary Science Database, zbMATH, DIALNET
  • Page Numbers: pp.621-636
  • Keywords: Matrix-geometric distribution, minimal signature, probability generating function, reliability, signature, RELIABILITY, DECOMPOSITIONS
  • Ankara University Affiliated: Yes

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.