Generalized Reliability Function for Systems of Arbitrary Configurations

In this note we consider a special system that always requires more than one elementary path between its input and output terminals to perform its job. Since the special system may consist of components that are not series-parallel connected, the generalized reliability function for systems of parallel components introduced by Chan is insufficient for studying the reliability of this class of systems. However, an even more generalized reliability function for the special system can be obtained by generalizing the path enumeration approach (path-tracing method). The conventional reliability function and the generalized reliability function of Chan are special cases of the one derived in this note.