Feasible star – delta and delta – star transformations for reliability networks

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Vishnuvajjula Charan Prasad

Consider the problem of transforming a star (delta) into an equivalent delta (star) in a reliability network with imperfect undirected edges and perfect vertices. It is believed that such transformations are not possible in general if the probabilities of the elements of the given star / delta are rational numbers. Contrary to this, it is shown here that star – delta and delta – star transformations are possible under certain conditions. Further the probability of success of an element of an equivalent star (delta) is shown to be equal to the probability of failure of the corresponding element of the given delta (star).

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