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Signatures of Coherent Systems Built with Separate Modules

Published online by Cambridge University Press:  14 July 2016

Ilya Gertsbakh*
Affiliation:
Ben Gurion University
Yoseph Shpungin*
Affiliation:
Shamoon College of Engineering
Fabio Spizzichino*
Affiliation:
Sapienza University of Rome
*
Postal address: Shai Agnon 30/25, 69362 Tel-Aviv, Israel. Email address: [email protected]
∗∗ Postal address: Department of Software Engineering, Shamoon College of Engineering, Beer Sheva, Bialik/Basel Streets, Beer Sheva, Israel. Email address: [email protected]
∗∗∗ Postal address: Department of Mathematics, Sapienza University of Rome, Piazzale Aldo Moro 2, 00185 Rome, Italy. Email address: [email protected]
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Abstract

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The signature is an important structural characteristic of a coherent system. Its computation, however, is often rather involved and complex. We analyze several cases where this complexity can be considerably reduced. These are the cases when a ‘large’ coherent system is obtained as a series, parallel, or recurrent structure built from ‘small’ modules with known signature. Corresponding formulae can be obtained in terms of cumulative notions of signatures. An algebraic closure property of families of homogeneous polynomials plays a substantial role in our derivations.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2011 

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