The detection of interactions is a challenging task present in almost all stages of software development. In feature-oriented system design, this task is mainly investigated for interactions of features within a single system, detected by their emergent behaviors. We propose a formalism to describe interactions in hierarchies of feature-oriented systems (hierarchical interactions) and the actual situations where features interact (active interplays). Based on the observation that such interactions are also crucial in role-based systems, we introduce a compositional modeling framework based on concepts and notions of roles, comprising role-based automata (RBAs). To describe RBAs, we present a modeling language that is close to the input language of the probabilistic model checker Prism. To exemplify the use of RBAs, we implemented a tool that translates RBA models into Prism and thus enables the formal analysis of functional and non-functional properties including system dynamics, contextual changes, and interactions. We carry out two case studies as a proof of concept of such analyses: First, a peer-to-peer protocol case study illustrates how undesired hierarchical interactions can be discovered automatically. Second, a case study on a self-adaptive production cell demonstrates how undesired interactions influence quality-of-service measures such as reliability and throughput.