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 is proposed for treating small output spaces which distinguishes between correctness and agreement. System reliability is investigated using analytical relationships and simulation. A consensus majority voting stratey is proposed and its performance is analyzed and compared with other voting strategies. A consensus voting strategy automatically adapts the voting to diffeerent component reliability and output space cardinality characteristics. It is shown that absolute majority voting strategy provides a lower bound on the reliability provided by the consensus majority, and the 2-of-n voting strategy an upper bound. If r is the cardinality of output space it is proved that 1/r is a lower bound on the average reliability of fault-tolerant system components below which the system reliability begins to deteriorate as more versions are added.