Journal of Applied Probability

Signatures of coherent systems built with separate modules

Ilya Gertsbakh, Yoseph Shpungin, and Fabio Spizzichino

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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.

Article information

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

First available in Project Euclid: 23 September 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 90B25: Reliability, availability, maintenance, inspection [See also 60K10, 62N05]

Cumulative and tail signatures recurrent series parallel system anchor homogeneous polynomial


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.

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