Novel method to construct large-scale design space in lubrication process utilizing Bayesian estimation based on a small-scale design-of-experiment and small sets of large-scale manufacturing data

A large-scale design space was constructed using a Bayesian estimation method with a small-scale design of experiments (DoE) and small sets of large-scale manufacturing data without enforcing a large-scale DoE. The small-scale DoE was conducted using various Froude numbers (X-1) and blending times (X-2) in the lubricant blending process for theophylline tablets. The response surfaces, design space, and their reliability of the compression rate of the powder mixture (Y-1), tablet hardness (Y-2), and dissolution rate (Y-3) on a small scale were calculated using multivariate spline interpolation, a bootstrap resampling technique, and self-organizing map clustering. The constant Froude number was applied as a scale-up rule. Three experiments under an optimal condition and two experiments under other conditions were performed on a large scale. The response surfaces on the small scale were corrected to those on a large scale by Bayesian estimation using the large-scale results. Large-scale experiments under three additional sets of conditions showed that the corrected design space was more reliable than that on the small scale, even if there was some discrepancy in the pharmaceutical quality between the manufacturing scales. This approach is useful for setting up a design space in pharmaceutical development when a DoE cannot be performed at a commercial large manufacturing scale.