Reliability Evaluation of the Design Space of the Granulation Process of Mefenamic Acid Tablets Using a Bootstrap Resampling Technique

The design space of the granulation process of mefenamic acid tablets, based on Box and Behnken design datasets, was described by a response surface method incorporating multivariate spline interpolation. The reliability of the optimal solutions and the acceptance ranges were evaluated by a bootstrap (BS) resampling technique. The distribution of the BS optimal solutions was almost symmetrical; however, several solutions, which were quite different from the original solution, were mixed. The reason for this problem was considered to be the mixing of the global and the local optima. Therefore, we applied self-organizing map (SOM) clustering for dividing data into several clusters and identified the cluster containing the global optima. The accuracy and reproducibility of the optimal solution in the cluster containing the optimal solution were quantitatively evaluated. In addition, the response surfaces modeled from all the BS datasets contained in the cluster were plotted into the same coordinates with the original response surface. The plots of BS optimal solutions were distributed around the original solution. Moreover, the average of all the BS response surfaces sufficiently corresponded with the original response surface. The conservative limits of the 95% confidence intervals of the acceptance ranges in three response variables could be calculated using the standard deviations of the BS response surfaces. Consequently, it was considered that a novel evaluation method based on BS resampling and SOM could be used for quantitatively evaluating the precision of the nonlinear response surface model.