Informal description (UML and text) of design patterns is adopted to facilitate their understanding by software developers. However, these descriptions lead to ambiguities, mainly when we consider Real time Design Patterns that deal with critical problems encountered in the design of real-time systems. Hence, there is a need for formal specification of the DPs and RTDPs to insure their successful application. In this paper, we propose a formalization approach of the system design based on real-time patterns (RTDPs). The processes of instantiation and composition of design patterns, permit us to generate design models (structural and dynamic) of complex systems. The resulting designs are represented in UML-MARTE profile to express the temporal properties and constraints. The algebraic specifications (in Maude language) become more natural and more efficient.