Bounds for two-terminal network reliability with dependent basic events

The two-terminal reliability problem has been a widely studied issue since 1970s. Therefore many efficient algorithms were proposed. Nevertheless, all these algorithms imply that all system components must be independent. With regard to nowadays applications it is not sufficient to assume independent component failures because in fault tolerant systems components may fail due to common cause failures or fault propagation. We therefore propose an algorithm which deals with upcoming dependencies. In addition to that, lower and upper bounds can be obtained in case the algorithm cannot be conducted until the end. The performance and accuracy of the algorithm is demonstrated on a certain network obeying a recursive structure where the exact result is given by a polynomial.