  The design space (DS) is defined as the combination of materials and process
conditions that guarantees the assurance of quality. This principle ensures
that as long as a process operates within DS, it consistently produces a
product that meets specifications. A novel DS identification method called the
R-DS identifier has been developed. It makes no assumptions about the
underlying model - the only requirement is that each model constraint (CQA)
should be approximated by a multivariate polynomial model. The method utilizes
the methodology of Rvachev's R-functions and allows for explicit analytical
representation of the DS with only a limited number of model runs. R-functions
provide a framework for representing complex geometric shapes and performing
operations on them through implicit functions. The theory of R-functions
enables the solution of geometric problem such as identification of DS through
algebraic manipulation. It is more practical than traditional sampling or
optimization-based methods. The method is illustrated using a batch reactor
system.
