The determination of the design space (DS) in a pharmaceutical process is a crucial aspect of the quality-by-design (QbD) initiative which promotes quality built into the desired product. This is achieved through a deep understanding of how the critical quality attributes (CQAs) and process parameters (CPPs) interact that have been demonstrated to provide quality assurance. For computational inexpensive models, the original process model can be directly deployed to identify the design space. One such crucial process is the Tablet Press (TP), which directly compresses the powder blend into individual units of the final product or adds dry or wet granulation to meet specific formulation needs. In this work, we identify the design space of input variables in a TP such that there is a (probabilistic) guarantee that the tablets meet the quality constraints under a set of operating conditions. A reduced-order model of TP is assigned for this purpose where the effects of lubricants and glidants are used to characterize the design space to achieve the desired tablet CQAs. The probabilistic design space, which takes into account interactions between crucial process parameters and important quality characteristics including model uncertainty, is also approximated because of the high cost associated with the comprehensive experiments.