Over the past decade the dynamic capabilities of self-adaptive software-intensive systems have proliferated and improved significantly. To advance the field of self-adaptive and self-managing systems further and to leverage the benefits of self-adaptation, we need to develop methods and tools to assess and possibly certify adaptation properties of self-adaptive systems, not only at design time but also, and especially, at run-time. In this paper we propose a framework for evaluating quality-driven self-adaptive software systems. Our framework is based on a survey of self-adaptive system papers and a set of adaptation properties derived from control theory properties. We also establish a mapping between these properties and software quality attributes. Thus, corresponding software quality metrics can then be used to assess adaptation properties.