Multidimensional Spectra of Multistate Systems with Binary Components

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.