Generalized decomposition method for complex systems

Many practical systems have complex structures that are not purely series, parallel, or series-parallel, such as communication networks, power plant control systems, electric power systems, computing systems, and etc. The emergence of those network redundant systems has been seen increasingly due to very high reliability requirements. The complex redundant techniques greatly improve system reliability, but also increase the difficulty in system reliability analysis to a great extent as well. For most of these practical complex systems, the existing methods give no way to obtain the expression of the system reliability, which is desire for design purpose. To deal with this problem, this paper proposes an approach generalized from the decomposition method, in which the conditional probability equation is extended from one key component to several keystones at a time. It has been found that the reliability of many complex systems becomes obtainable in this way, especially for the complex networks with certain structural patterns. The general reliability expression of the proposed method is given in this paper. The method is illustrated by examples, and the power of the method is demonstrated by applying it to a real complex system.