Bilateral estimates of the effectiveness retention ratio of the systems with output effect depending on the number of executive elements

Very simple bilateral estimates of the effectiveness retention ratio for a wide class of complex systems with the output effect determined by the number of normally operating executive elements were proposed. Such systems are represented, for example, by the information control systems having hierarchical branching structure, queuing systems, and communication systems. To establish the estimates, it suffices to know only the expectation of the number of normally operating executive elements. At that, admitted are statistical dependencies between the states of the system elements and arbitrary nature of the flows of failures and recovery of the elements.