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  • Signatures of Coherent Systems Built with Separate Modules

  • Part of
  • Ilya Gertsbakh, Yoseph Shpungin, Fabio Spizzichino
  • Journal:
    Journal of Applied Probability / Volume 48 / Issue 3 / September 2011
    Published online by Cambridge University Press:
    14 July 2016, pp. 843-855
    Print publication:
    September 2011
    • Article
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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.