Reliability in Digital Systems with Asymmetrical Failure Modes

Most present-day reliability schemes using redundancy to mask the failure of individual logic modules employ majority voting with the assumption that the replicated modules have symmetrical failure characteristics. An analysis is presented of such schemes when the modules exhibit asymmetrical failure modes; that is, the probability that a module fails with a 0 output is not equal to the probability that it fails with a 1 output. A general expression is presented which gives the reliability of a network consisting of n identical modules feeding a k-out-of-n voter. It is shown that a simple majority element does not always represent the optimal choice. Plots illustrating the results are included.