Unpredictable changes continuously affect software systems and may have a severe impact on their quality of service, potentially jeopardizing the system's ability to meet the desired requirements. Changes may occur in critical components of the system, clients' operational profiles, requirements, or deployment environments.

The adoption of software models and model checking techniques at run time may support automatic reasoning about such changes, detect harmful configurations, and potentially enable appropriate (self-)reactions. However, traditional model checking techniques and tools may not be simply applied as they are at run time, since they hardly meet the constraints imposed by on-the-fly analysis, in terms of execution time and memory occupation.

This paper precisely addresses this issue and focuses on reliability models, given in terms of Discrete Time Markov Chains, and probabilistic model checking. It develops a mathematical framework for run-time probabilistic model checking that, given a reliability model and a set of requirements, statically generates a set of expressions, which can be efficiently used at run-time to verify system requirements. An experimental comparison of our approach with existing probabilistic model checkers shows its practical applicability in run-time verification.