What is the theory of bounds for network reliability

At present “the theory of bounds for network reliability” is absorbed by a more wide theory of network reliability (in one’s turn, by a theory of reliability). It is not an independent subject. In spite of monographs on reliability theory (see, for example, [1,2,3,4]) pay some attention to bounds of network reliability, it is difficult to realize the subject clearly. Nobody describes it systematically. Moreover, the subject was never a whole object for independent investigation. Of course, presentations there exist (see, for example, [4]). Recently we made an attempt to give [5] a general look on the subject. Here are its essential features