The cost of software maintenance is always increasing. The companies are often confronted to failures and software errors. The quality of software to use is so required. In this paper, the authors propose a new formal approach for assessing the quality of object-oriented system design according to the quality assessment model. This approach consists in modeling the input software system by an automaton based on object-oriented design metrics and their relationship with the quality attributes. The model exhibits the importance of metrics through their links with the attributes of software quality. In addition, it is very practical and flexible for all changes. It allows the quality estimation and its validation. For the verification of proposed probabilistic model (automaton), they use the model-checking and the prism tool. The model-checking is very interesting for the evaluation and validation of the probabilistic automaton. They use it to approve the software quality of the three experimental projects. The obtained results are very interesting and of great importance.