## Journal of Applied Probability

### Signatures of coherent systems built with separate modules

#### Abstract

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.

#### Article information

Source
J. Appl. Probab., Volume 48, Number 3 (2011), 843-855.

Dates
First available in Project Euclid: 23 September 2011

https://projecteuclid.org/euclid.jap/1316796919

Digital Object Identifier
doi:10.1239/jap/1316796919

Mathematical Reviews number (MathSciNet)
MR2884820

Zentralblatt MATH identifier
1230.60096

#### Citation

Gertsbakh, Ilya; Shpungin, Yoseph; Spizzichino, Fabio. Signatures of coherent systems built with separate modules. J. Appl. Probab. 48 (2011), no. 3, 843--855. doi:10.1239/jap/1316796919. https://projecteuclid.org/euclid.jap/1316796919

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