In the era of Big Data, more and more stream data is available. In the same way, Decision Support Systems (DSS) tools, such as data warehouses and alert systems, become more and more sophisticated, and conceptual modeling tools are consequently mandatory for successfully DSS projects. Formalisms such as UML and ER have been widely used in the context of classical information and data warehouse systems, but they have not been investigated yet for stream data warehouses to deal with alert systems. Therefore, in this article, the authors introduce the notion of Active Stream Data Warehouse (ASDW) and this article proposes a UML profile for designing Active Stream Data Warehouses. Indeed, this article extends the ICSOLAP profile to take into account continuous and window OLAP queries. Moreover, this article studies the duality of the stream and OLAP decision-making process and the authors propose a set of ECA rules to automatically trigger OLAP operators. The UML profile is implemented in a new OLAP architecture, and it is validated using an environmental case study concerning the wind monitoring.