One of the main objectives of developing component-based software systems is to enable efficient building of systems through the integration of components. All component models define some form of component inter-face standard that facilitates the programmatic integration of components, but they do not facilitate or provide theories for the prediction of the quality attributes of the component compositions. This decreases significantly the value of the component-based approach to building dependable systems. If it is not possible to predict the value of a particular attribute of a system prior to integration and deployment to the target environment the system must be subjected to other procedures, often costly, to determine this value empirically. For this reason one of the challenges of the component-based approach is to obtain means for the "composition" of quality attributes. This challenge poses a very difficult task because the diverse types of quality attributes do not have the same underlying conceptual characteristics, since many factors, in addition to component properties, influence the system properties. This paper analyses the relation between the quality attributes of components and those of their compositions. The types of relations are classified according to the possibility of predicting properties of compositions from the properties of the components and according to the influences of other factors such as software architecture or system environment. The classification is exemplified with particular cases of compositions of quality attributes, and its relation to dependability is discussed. Such a classification can indicate the efforts that would be required to predict the system attributes which are essential for system dependability and in this way, the feasibility of the component-based approach in developing dependable systems.