A scenario-based development approach has become state of the art for automated driving systems. Once a set of scenario classes covering the operational design domain is available, concrete scenarios are generated from these scenario classes, e.g., to be used for hazard analysis and risk assessment or for the system's verification and validation. For such applications, a high diversity among the generated concrete scenarios is paramount. The question arises how the quality of collections of concrete scenarios can be assessed in such a setting. In this work, we aggregate scenario distance measures into so-called quality functions that quantify the diversity of concrete scenario collections in the context of automated driving. In particular, we consider the case where scenario classes are formalized as constraint systems and the associated concrete scenario space is not explicitly known. Based on a set of desired properties we construct candidates for such quality functions and give proofs for their property fulfillment. To show the practical relevance of quality functions, we perform a variety of experiments in the context of an abstract scenario-based virtual verification toolchain for automated driving systems. More specifically, we use quality functions to compare the effectiveness of variation methods for sampling, examine the choice of different scenario distance measures, and investigate the effects of temporal aspects on concrete scenario collection quality.

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