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Signatures and D-spectra and Their Use in Reliability Calculations: A Review

Volume 8, Number 4, July 2012 - Paper 3 - pp. 367 - 378

ILYA B. GERTSBAKH1 and YOSEPH SHPUNGIN2

1 Department of Mathematics, Ben-Gurion University
  P. O. Box 653, Beer-Sheva, 84105, Israel
2 Software Engineering Department
  Sami Shamoon College of Engineering, Beer Sheva 84100 Israel

(Received on March 06, 2011 and revised on July 22, 2011 and May 19, 2012)

Abstract:

Coherent systems with binary components have important structural parameters known in literature as signatures and D-spectra. The knowledge of these parameters allows to obtain the probabilistic description of coherent systems behavior in the process of their component failures, and such system characteristics as probabilistic resilience, component importance, system failure probability as a function of component failure probability q, approximations to system reliability, and the bounds on system reliability if we know only the bounds on q.

When the system has many components, the exact calculation of signatures or D-spectra becomes a very complicated issue. We suggest the use for their approximation efficient Monte Carlo procedures. All relevant calculations are illustrated by examples of networks.

This paper provides a nonformal review of relevant literature and the methodology of reliability calculations, based mostly on recently published books and research papers.

 

References: 19

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