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Signatures of Coherent Systems Built with Separate Modules

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Ilya Gertsbakh ,
Yoseph Shpungin  and
Fabio Spizzichino
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.

Keywords

Cumulative and tail signaturesrecurrentseriesparallel systemanchorhomogeneous polynomial

MSC classification

Secondary: 60K10: Applications (reliability, demand theory, etc.) 90B25: Reliability, availability, maintenance, inspection
Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 3 , September 2011 , pp. 843 - 855
Copyright
Copyright © Applied Probability Trust 2011 

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