On Optimal Redundancy of Multivalue-Output Systems

This paper considers improving the reliability of multivalue-output systems by the use of n-redundant systems in which n copies of systems are used redundantly and the output is determined from the outputs of those copies by the voter. A k-out-of-n redundant system minimizes the mean loss caused by the occurrence of output errors under the condition that the voter can be composed of only two kinds of operators, logical sum and logical product. The optimal k depends on the probability and loss matrices, but it can be specified in some special cases. The mean loss of multivalue-output systems with multichannels can be minimized by adopting k-out-of-n redundancy for each channel. The results provide a powerful guide to the improvement of fail-safe characteristics of many systems and the design of fault-tolerant systems.