Formulas for estimating the reliability of dynamic info-communication network with dependent components

Goal. To create a mathematical tool for assessing the quality of a complex system likely availability (or failure) in the presence of interrelation in the components operation. The tool is different from the Markov's chain and other analogs. Tasks. To introduce a binomial distribution as the sum of the probabilities of ordered subsets of the numbers of successful tests. Introduction to probability of success of the multidimensional parameter influence on the behavior of the system components. The resulting expression generalizes author's previously obtained results. Methods. Analytical transformation of the binomial scheme and its modifications. The method of probabilistic characteristic functions. Results. It is obtained generalized formulas are suitable as equivalent models in statistical diagrams model the behavior of complex systems with network architecture. Formulas can programmed for estimating probabilities of failure of a particular set of components (routes) or overall systems.