  Experiments with both qualitative and quantitative factors occur frequently
in practical applications. Many construction methods for this kind of designs,
such as marginally coupled designs, were proposed to pursue some good
space-filling structures. However, few criteria can be adapted to quantify the
space-filling property of designs involving both qualitative and quantitative
factors. As the uniformity is an important space-filling property of a design,
in this paper, a new uniformity criterion, qualitative-quantitative discrepancy
(QQD), is proposed for assessing the uniformity of designs with both types of
factors. The closed form and lower bounds of the QQD are presented to calculate
the exact QQD values of designs and recognize the uniform designs directly. In
addition, a connection between the QQD and the balance pattern is derived,
which not only helps to obtain a new lower bound but also provides a
statistical justification of the QQD. Several examples show that the proposed
criterion is reasonable and useful since it can distinguish distinct designs
very well.
