A Simpler and More Direct Derivation of System Reliability Using Markov Chain Usage Models

Abstract

Markov chain usage-based statistical testing has been around for more than two decades, and proved sound and effective in providing audit trails of evidence in certifying software-intensive systems. The system end-to-end 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 reviews the analytical derivation of the single use reliability mean, and proposes a simpler, faster, and more direct way to compute the expected value that renders an intuitive explanation. The new derivation is illustrated with two examples.