Trustworthiness in systems is of paramount importance. Among safety modeling languages, Markov chains are a good tradeoff between the safety concepts that can be modeled and the ease of calculation. However, as they model the different states of the systems, they suffer from the state space explosion. This explosion has two drawbacks: it makes Markov chains very difficult to write by hand for large systems, and large Markov chain calculation is resource consuming. The first drawback is easily tackled by generating Markov chains from higher-level languages (such as AltaRica 3.0).

In this thesis, we focused on the partial generation of Markov chains, to tackle the state space explosion of the models. This idea is based on the observation that even large repairable systems spent most of their times in a few number of states, that are close to the nominal state of the system. The partial generation is based on Dijkstra's algorithm and on a so-called relevance factor to generate only the most probable states of the Markov chain. The reliability indicators obtained with such a partial chain can be bounded with a slightly different Markov chain.

The partial generation method is fully implemented in the AltaRica 3.0 project to automatically calculate the reliability indicators of a system modeled in AltaRica. Different experiments illustrate the practability of the method, as well as its strengths and weaknesses.

Pierre-Antoine BRAMERET