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D-SPECTRUM AND RELIABILITY OF A BINARY SYSTEM WITH TERNARY COMPONENTS

Published online by Cambridge University Press:  14 October 2015

Ilya B. Gertsbakh ,
Yoseph Shpungin  and
Radislav Vaisman
Ilya B. Gertsbakh
Affiliation:
Department of Mathematics, Ben-Gurion University, P. O. Box 653, Beer-Sheva 84105, Israel E-mail: [email protected]
Yoseph Shpungin
Affiliation:
Software Engineering Department, Sami Shamoon College of Engineering, Beer Sheva 84100, Israel E-mail: [email protected]
Radislav Vaisman
Affiliation:
School of Mathematics and Physics, The University of Queensland, Brisbane 4072, Australia E-mail: [email protected]
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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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 30 , Issue 1 , January 2016 , pp. 25 - 39
Copyright
Copyright © Cambridge University Press 2015 

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