Socio-technical systems are increasingly becoming software-intensive. The challenge now is to design the architecture of such software-intensive systems for guaranteeing not only its correctness, but also the correctness of its implementation. In social-technical systems, the architecture (including software and physical elements) is described in terms of Piping and Instrumentation Diagrams (P&ID). The design of these P&ID is still considered an art for which no rigorous design support exists. In order to detect and eliminate architectural design flaws, this paper proposes a formal-based automated approach for the verification of the essential architecture “total correctness” properties, i.e. compatibility, completeness, consistency, and correctness. This approach is based on the definition of an architectural style for P&ID design in Alloy. We use MDE to automatically generate Alloy models from a P&ID and check their compatibility with the style and its completeness, consistency, and correctness properties. Our approach is presented through an industrial case study: the system of storage and production of freshwater for a ship.