Technical textiles, in particular, nonwovens used, for example, in medical masks, have become increasingly important in our daily lives. The quality of these textiles depends on the manufacturing process parameters that cannot be easily optimized in live settings. In this article, we present a visual analytics framework that enables interactive parameter space exploration and parameter optimization in industrial production processes of nonwovens. Therefore, we survey analysis strategies used in optimizing industrial production processes of nonwovens and support them in our tool. To enable real-time interaction, we augment the digital twin with a machine learning surrogate model for rapid quality computations. In addition, we integrate mechanisms for sensitivity analysis that ensure consistent product quality under mild parameter changes. In our case study, we explore the finding of optimal parameter sets, investigate the input-output relationship between parameters, and conduct a sensitivity analysis to find settings that result in robust quality.