Looking for a hyper polyhedron within the multidimensional space of Design Space from the results of Designs of Experiments

• Published in: Chemometrics and intelligent laboratory systems Vol. 232; p. 104712
• Main Authors: Manzon, Diane, Ghattas, Badih, Claeys-Bruno, Magalie, Declomesnil, Sophie, Carité, Christophe, Sergent, Michelle
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.01.2023; Elsevier
• Subjects: Design of Experiments (DoE); Design Space (DS); Mathematics; Proven Acceptable Independent Range (PAIR); Quality by Design (QbD); Quantitative Finance; Response Surface Methodology (RSM); Quality by Design (QbD); Design of Experiments (DoE); Response Surface Methodology (RSM); Proven Acceptable Independent Range (PAIR); Design Space (DS)
• ISSN: 0169-7439; 1873-3239
• DOI: 10.1016/j.chemolab.2022.104712

In pharmaceutical studies, the Quality by Design (QbD) approach is increasingly being implemented to improve product development. Product quality is tested at each step of the manufacturing process, allowing a better process understanding and a better risk management, thus avoiding manufacturing defects. A key element of QbD is the construction of a Design Space (DS), i.e., a region in which the specifications on the output parameters should be met. Among the various possible construction methods, Designs of Experiments (DoE), and more precisely Response Surface Methodology, represent a perfectly adapted tool. The DS obtained may have any geometrical shape; consequently, the acceptable variation range of an input may depend on the value of other inputs. However, the experimenters would like to directly know the variation range of each input so that their variation domains are independent. In this context, we developed a method to determine the “Proven Acceptable Independent Range” (PAIR). It consists of looking for all the hyper polyhedra included in the multidimensional DS and selecting a hyper polyhedron according to various strategies. We will illustrate the performance of our method on different DoE cases. •The establishment of Design Space is a key step of Quality by Design approach.•The determination of a hyper polyhedron included in the Design Space is proposed.•The “Proven Acceptable Independent Ranges” of each input parameter are defined.