Sensors in smart-item environments capture data about product conditions and usage to support business decisions as well as production automation processes. A challenging issue in this application area is the restricted quality of sensor data due to limited sensor precision and sensor failures. Moreover, data stream processing to meet resource constraints in streaming environments introduces additional noise and decreases the data quality. In order to avoid wrong business decisions due to dirty data, quality characteristics have to be captured, processed, and provided to the respective business task. However, the issue of how to efficiently provide applications with information about data quality is still an open research problem. In this article, we address this problem by presenting a flexible model for the propagation and processing of data quality. The comprehensive analysis of common data stream processing operators and their impact on data quality allows a fruitful data evaluation and diminishes incorrect business decisions. Further, we propose the data quality model control to adapt the data quality granularity to the data stream interestingness.