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The Moore-Shannon model for switching circuits is extended to show how the number of redundant relays needed to improve reliability depends on the logical function of the entire circuit. The reliabilities of and, or, and exclusive-or relay circuits are studied as a function of the number of relays, the network topology, and the distribution of inputs. For the case of intermittent failures, a procedure is developed for calculating the reliability of combinational switching circuits, defined as the probability that the circuit will function as specified, averaged over all possible inputs, and subject to the idealizing assumptions of the Moore-Shannon model. The redundancies required to achieve a specified increase in reliability, although considerably smaller than for alternative methods, are still enormous. It is shown that a good way to improve an and circuit, for example, is to use a series-parallel network in which the number of parallel lines varies with the logarithm of the number of basic and circuits connected in series to form each line.
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