D-spectrum and reliability of a binary system with ternary components

Gertsbakh, Ilya B, Shpungin, Yoseph and Vaisman, Radislav (2015) D-spectrum and reliability of a binary system with ternary components. Probability in the Engineering and Informational Sciences, 30 1: 25-39. doi:10.1017/S0269964815000261

Author Gertsbakh, Ilya B
Shpungin, Yoseph
Vaisman, Radislav
Title D-spectrum and reliability of a binary system with ternary components
Journal name Probability in the Engineering and Informational Sciences   Check publisher's open access policy
ISSN 0269-9648
Publication date 2015-10-14
Year available 2015
Sub-type Article (original research)
DOI 10.1017/S0269964815000261
Open Access Status Not Open Access
Volume 30
Issue 1
Start page 25
End page 39
Total pages 15
Place of publication Cambridge, United Kingdom
Publisher Cambridge University Press
Language eng
Formatted abstract
We consider a monotone binary system with ternary components. “Ternary” means that each component can be in one of three states: up, middle (mid) and down. Handling such systems is a hard task, even if a part of the components have no mid state. Nevertheless, the permutation Monte Carlo methods, that proved very useful for dealing with binary components, can be efficiently used also for ternary monotone systems. It turns out that for “ternary” system there also exists a combinatorial invariant by means of which it becomes possible to count the number C(r;x) of system failure sets which have a given number r and x of components in up and down states, respectively. This invariant is called ternary D-spectrum and it is an analogue of the D-spectrum (or signature) of a system with binary components. Its value is the knowledge of system failure or path set properties which do not depend on stochastic mechanism governing component failures. In case of independent and identical components, knowing D-spectrum makes it easy to calculate system UP or DOWN probability for a variety of UP/DOWN definitions suitable for systems of many types, like communication networks, flow and supply networks, etc
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2016 Collection
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