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Computing minimal signature of coherent systems through matrix-geometric distributions

Part of: Special processes Survival analysis and censored data

Published online by Cambridge University Press:  16 September 2021

Serkan Eryilmaz Open the ORCID record for Serkan Eryilmaz [Opens in a new window]  and
Fatih Tank
Serkan Eryilmaz*
Affiliation:
Atilim University
Fatih Tank*
Affiliation:
Ankara University
*
*Postal address: Atilim University, Department of Industrial Engineering, Ankara, Turkey. Email address: serkan.eryilmaz@atilim.edu.tr
**Postal address: Ankara University, Department of Actuarial Sciences, Ankara, Turkey. Email address: tank@ankara.edu.tr
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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.

Keywords

Matrix-geometric distributionminimal signatureprobability generating functionreliabilitysignature

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Original Article
Information
Journal of Applied Probability , Volume 58 , Issue 3 , September 2021 , pp. 621 - 636
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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