Open & Short Circuit Reliability of Systems of Identical Items

The paper is about reliability and risk analysis of systems of s-identical, s-independent items in terms of their probabilities of failure in open and short circuit. It is importantly assumed that the system is operational while at least one (or as a special case, more) operational item is connected physically to the input and output of the system either directly or through other good or shorted items and there is no overall system short-circuit. Two or more items so connected, whether in physical series or parallel or any combination have the same effect as a single item, and such redundancy does not alter the item failure probabilities. The probabilities could be those arising from identical, s-independent distributions (iid) over a fixed period with fixed starting conditions or alternatively probabilities of failure upon switching on. The work applies therefore to systems of adjustable or self-adjusting items such as amplifiers, rheostats, or fluid control valves, but not, for example, to systems of fixed resistors if the output values of voltage and current are important. Methods are developed for finding the most reliable physical arrangements of 2, 3, 4, items given the item failure probabilities. These display symmetry arising from the equivalence of the reliability block diagrams for items in physical series failing short and items in physical parallel failing open and vice versa. Three or four items are often sufficient to meet reliability requirements.