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.

翻译：设计空间（DS）被定义为能够确保质量保证的材料与工艺条件的组合。该原则保证只要工艺在设计空间内运行，就能持续生产出符合规格的产品。本文提出了一种称为R-DS识别器的新型设计空间识别方法。该方法不对底层模型作任何假设——唯一要求是每个模型约束（关键质量属性）需通过多元多项式模型进行近似。该方法运用Rvachev的R函数方法论，仅需有限次模型运行即可实现设计空间的显式解析表达。R函数为复杂几何形状的隐函数表示及其运算提供了框架。R函数理论使得通过代数运算解决设计空间识别等几何问题成为可能。相比传统的基于抽样或优化的方法，本方法更具实用性。本文以间歇反应器系统为例对该方法进行了说明。