Robust design modeling and optimization of a multi-response time series for a pharmaceutical process

Robust design (RD) methods, which are based upon the concept of building quality into products or processes, are increasingly popular in the science and engineering research communities. One particular area of RD research that has not received considerable attention is in working with multiple time series responses, observed frequently within the field of pharmaceutical science. In order to determine the optimal pharmaceutical formulation, or input factor settings, suitable robust experimental design and analysis methods must be performed. To achieve this objective, the primary aim of this paper is to propose a new methodology that specifically addresses the multi-response time series problem for a pharmaceutical formulation process. First, an experimental format and framework for testing drug release kinetics is proposed by implementing a mixture experimental design and time series response modeling. Second, an alternative robust design model is developed to identify the optimal pharmaceutical formulation, based upon the time series target profiles for drug release kinetics. Finally, a case study associated with a drug development process is performed to validate the proposed model. The results of this case study indicate that the optimal drug release kinetics is significantly similar to the target profile.