Efficient monitoring of a cloud system involves multiple aggregation processes and large amounts of data with various and interdependent requirements. A thorough understanding and analysis of the characteristics of data aggregation processes can help to improve the software quality and reduce development cost. In this paper, we propose a systematic approach for designing data aggregation processes in cloud monitoring systems. Our approach applies a feature-oriented taxonomy called DAGGTAX (Data AGGregation TAXonomy) to systematically specify the features of the designed system, and SAT-based analysis to check the consistency of the specifications. Following our approach, designers first specify the data aggregation processes by selecting and composing the features from DAGGTAX. These specified features, as well as design constraints, are then formalized as propositional formulas, whose consistency is checked by the Z3 SAT solver. To support our approach, we propose a design tool called SAFARE (SAt-based Feature-oriented dAta aggREgation design), which implements DAG-GTAX-based specification of data aggregation processes and design constraints, and integrates the state-of-the-art solver Z3 for automated analysis. We also propose a set of general design constraints, which are integrated by default in SAFARE. The effectiveness of our approach is demonstrated via a case study provided by industry, which aims to design a cloud monitoring system for video streaming. The case study shows that DAGGTAX and SAFARE can help designers to identify reusable features, eliminate infeasible design decisions, and derive crucial system parameters.