Component based development of software systems needs to devise effective test management strategies in order fully achieve its perceived advantages of cost efficiency, flexibility, and quality in industrial contexts. In industrial systems with quality demands, while testing software, measures are employed to evaluate the thoroughness achieved by execution of a certain set of test cases. Typically, these measures are expressed in the form of coverage of different structural test criteria, e.g., statement coverage. However, such measures are traditionally applicable only on the lowest level of software integration (i.e., the component level). As components are assembled into subsystems and further into full systems, general measures of test thoroughness are no longer available. In this context, we formalize the added test effort and show to what extent the coverage of structural test criteria are maintained when components are integrated, in three representative component models. This enables focusing on testing the right aspects of the software at the right level of integration, and achieves cost reduction during testing one of the most resource-consuming activities in software engineering.