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Paper IPM / M / 15541  


Abstract:  
The signature matrix of an ncomponent threestate network (system), which depends only on the network structure, is a useful tool for comparing the reliability and stochastic properties
of networks. In this paper, we consider a threestate network with states up, partial performance, and down. We assume that the network remains in state up, for a random time T 1 and then moves to state partial performance until it fails at time T > T 1 . The signaturebased expressions for the conditional entropy of T given T 1 , the joint entropy, KullbackLeibler (KL)
information, and mutual information of the lifetimes T and T 1 are presented. It is shown that the KL information, and mutual information between T 1 and T depend only on the network structure (i.e., depend only to the signature matrix of the network). Some signaturebased
stochastic comparisons are also made to compare the KL of the state lifetimes in two different threestate networks. Upper and lower bounds for the KL divergence and mutual information between T 1 and T are investigated. Finally the results are extended to ncomponent multistate networks. Several examples are examined graphically and numerically.
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