Reliability Limits of Three-Sensor Majority Voting under Correlated Errors and Voter Faults

Abstract

Three-sensor majority voting can improve the reliability of binary decisions, but its effectiveness depends on sensor error dependence and voter reliability. This paper presents an analytical model that combines independent sensor errors with a shared-error mode and represents voter faults as independent reversals of the majority decision. Closed-form expressions are derived for the system error probability, the voter fault threshold below which redundancy outperforms a single sensor, and the maximum dependence level compatible with a specified reliability target. Within the proposed mixture model, the benefit of redundancy decreases linearly with pairwise error correlation. Illustrative calculations show that even a small voter fault probability can substantially increase the error of an otherwise reliable sensor subsystem. An exchangeable-distribution counterexample further demonstrates that identical marginal error probabilities and pairwise correlations can produce different majority-vote error probabilities. These findings highlight the need to characterize joint sensor errors and explicitly account for voter faults when evaluating redundant sensing architectures. The study is theoretical; the numerical examples are calculated from assumed parameters and do not represent experimental measurements.