Optimal `series-parallel´ networks of 3-state devices

A 3-state component is one which can fall in two different modes: an open mode and a shorted mode. Systems built from such components can also experience either of these two failure modes. For a given number of s-identical s-independent components, a pure `series´ or pure `parallel´ configuration would be most reliable if only one of the two failure modes were possible. This paper treats the problem of designing the most reliable configuration of a given number of s-identical components that can experience both failure modes. Two simple algorithms for designing an optimal configuration are presented, and by analysis of 6, 8, and 20-component systems they illustrate the extent to which other configurations can be more reliable than `series-parallel´ or `parallel-series´ arrays