Boolean functions with engineering applications and computer programs
Boolean functions with engineering applications and computer programs
Fault Tree Analysis - A Bibliography
Fault Tree Analysis - A Bibliography
n-tuples of 0s and 1s: necessary and sufficient conditions for intrinsic order
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartI
A picture for complex stochastic boolean systems: the intrinsic order graph
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part III
A new algorithm for complex stochastic boolean systems
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
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This paper deals with the reliability and risk analysis of those complex systems depending on nstochastic Boolean variables. Each one of the 2nelementary states associated to such a system is given by its corresponding binary n-tuple of 0s and 1s. A symmetric fractal graph on 2nnodes (the so-called intrinsic order graph In) is used for displaying all the binary n-tuples in decreasing order of their occurrence probabilities. The successive bisections of this graph into smaller subgraphs one-to-one correspond to the successive splits of 1 as sum of the occurrence probabilities of those subgraphs. This iterative bisection process satisfies a nice property: if we replace each one of the subgraphs C(obtained after ksuccessive bisections of the original intrinsic order graph In) by an unique node weighted by the sum of the probabilities of all vertices lying on Cand we sort the new nodes in decreasing order of their weights, then the new condensed graph is exactly the intrinsic order graph Ik. Finally, based on these results, a new algorithm for estimating the unavailability of stochastic Boolean systems is presented.