Reliability of voting in fault-tolerant software systems for small output-spaces

Under a voting strategy in a fault-tolerant software system there is a difference between correctness and agreement. An independent N-version programming reliability model which distinguishes between correctness and agreement is proposed for treating small output spaces. An alternative voting strategy, consensus voting, is used to treat cases when there can be agreement among incorrect outputs, a case which can occur with small output spaces. The consensus voting strategy automatically adapts the voting to various version reliability and output-space cardinality characteristics. The majority-voting strategy provides reliability which is a lower bound, and the 2-out-of-n voting strategy provides reliability which is an upper bound, on the reliability by consensus voting. The reciprocal of the cardinality of output space is a lower bound on the average reliability of fault-tolerant system versions below which the system reliability begins to deteriorate as more versions are added.< >