Considering Dependent Components in the Terminal Pair Reliability Problem
The determination of the reliability value for technical systems whose components are subjected to random failure possesses a wide range of applicability, e.g. in data communication networks, computer architectures and electrical power networks. The inherent redundancy structures can be described by reliability block diagrams (RBDs) and by solving those RBDs the reliability of the respective system can be computed. The problem of solving the RBD in order to compute the reliability is well-known as the terminal pair reliability problem. If it is assumed that system components fail independently, pure combinatorial methods can be applied to determine the required probability. However, as soon as there are some dependencies concerning the failure of components we cannot utilize pure combinatorial methods unless we do some suitable modifications which take the dependencies into account. For this purpose we present a hybrid method based on the idea of factoring in combination with series and parallel reductions for systems with dependent component failures. The method is hybrid in the sense that dependent probability terms arisen from our proposed algorithm can be obtained by the help of a stochastic solver. The algorithm comprises clauses for carrying out series and parallel reductions in parallel with factoring. In addition to that we propose how to deal with multiple occurring components.