Threshold systems and their reliability

A threshold system is defined as a system whose success/failure is a threshold swithching function in the successes/failures of its components. Examples of such a system abound in applications involving decision mechanisms or involving supply-type components with fixed ratings for their capacity, flow, throughput, and the like. In general, a threshold system can be coherent or noncoherent. If a coherent threshold system is made to have identical component weights, then it reduces to the well known k-out-of-n or voting system. The paper lists some of the fundamental properties of a threshold system, and presents a recursive algorithm for computing the exact system reliability. Illustrative examples are given, and extension to the multi-threshold case is also discussed.