Multidimensional Spectra of Multistate Systems with Binary Components

Ilya Gertsbakh () and Yoseph Shpungin ()
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Ilya Gertsbakh: Ben Gurion University of the Negev
Yoseph Shpungin: Sami Shamoon College of Engineering

Chapter Chapter 4 in Recent Advances in System Reliability, 2012, pp 49-61 from Springer

Abstract: Abstract We consider coherent systems with K > 1 UP states and binary components. Introducing uniform measure on $$ n! $$ permutations of component numbers, we define a system’s combinatorial invariant, so-called multidimensional D-spectrum. By means of its marginal distributions we determine the probability that the system is in state $$ i \in [0,1,2, \ldots ,K] $$ , where 0 denotes system DOWN state. Formulas establishing the connection between the cumulative D-spectra and the number of system failure sets are derived. We present an example of a four-dimensional cubic network with 16 nodes, 32 edges and four terminals and the probabilistic description of its disintegration into four isolated clusters in the process of random edge failures.

Keywords: Multistate coherent systems; Multidimensional D-spectra; Signatures; State probabilities (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4471-2207-4_4

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