Optimizing simple circuitry for reliability and performance by failure mode

Abstract

MANY PAPERS have been written about redundant circuits in which components can undergo either open-circuit or short-circuit failure. John von Newmann studied the problem in connection with abstract automata.1 Shannon and Moore showed that any given reliability could be achieved by using redundancy, however, as the reliability approaches 1, the number of parts involved approaches infinity.2 Other papers have been written that derive the formulas for mean time to failure and/or reliability for series-parallel and parallel-series type arrangements, that is, for n items in series and m such arrangements of n items in parallel, or n items in parallel and n such arrangements of n items in series.3,4 In applications to either ground-based equipment or microminiaturized parts such analysis is sufficient. However, there is not a true optimization until all circuits are considered. In systems with tight size, weight, and power requirements, all circuits must be considered. This paper discusses all circuits containing four components or less. Graphs are presented showing the circuit's optimizing reliability for any component reliability distribution. Then the exponential distribution is assumed, and the circuits maximizing the expected life are found. In both these optimization procedures, there will be optimal circuits which are not of the parallel-series or series-parallel type.