On A Simpler and Faster Derivation of Single Use Reliability Mean and Variance for Model-Based Statistical Testing

Abstract

Markov chain usage-based statistical testing has proved sound and effective in providing audit trails of evidence in certifying software-intensive systems. The system end-toend reliability is derived analytically in closed form, following an arc-based Bayesian model. System reliability is represented by an important statistic called single use reliability, and defined as the probability of a randomly selected use being successful. This paper continues our earlier work on a simpler and faster derivation of the single use reliability mean, and proposes a new derivation of the single use reliability variance by applying a well-known theorem and eliminating the need to compute the second moments of arc failure probabilities. Our new results complete a new analysis that could be shown to be simpler, faster, and more direct while also rendering a more intuitive explanation. Our new theory is illustrated with three simple Markov chain usage models with manual derivations and experimental results.