Trivariate Bernoulli distribution with application to software fault tolerance

The widespread reliance on software for mission and life critical applications makes the reliability of these systems essential. Techniques such as fault tolerance have been proposed to achieve the highest levels of software reliability. However, the fault tolerance paradigm suffers from the risk of correlated failures, where a majority of the software versions fail on the same input leading to system failure. This paper derives a trivariate Bernoulli distribution to quantify the negative impact of correlated failures on the reliability of fault tolerant software composed of highly reliable versions. An experiment based on early empirical research demonstrates the capacity of the distribution to conduct reliability assessment for many combinations of the version reliabilities and correlations. The results indicate that correlated failures detract from system reliability, but that this reliability is often higher than a system composed of the single most reliable version.