Augmented study approach
The screening-study analysis helped determine a model equation that successfully describes the design space. The hardness
and tablet weight models had R
values close to 100%. The models were significant, with at least 95% confidence in the results. The centerpoint runs showed
minor curvature in the design space, and an augmented experimental study with additional centerpoints would help determine
its effect, since only three centerpoint runs were performed during the screening study. The screening study also showed no
evidence that an upper or lower limit had been reached for the hardness or the tablet weight. An augmented study allows for
the outer limits of the original screening study to be broadened to expand the factor limits and eventually aid in optimization.
A central composite design (CCD) was selected for the augmented study to enable a response-surface method approach to optimization.
Design-Expert software was used to prepare the augmented study factor limits and experimental run sheets. For the augmented
study, an additional 15 runs were added to the original screening study of 19 runs, with new upper and lower limits. The 15
augmented runs included five centerpoint runs. For the 10 remaining runs that were not centerpoints, each factor was set at
the new upper or lower limit, while the other four factors were set to their midpoints.
The limits for the augmented study are shown in Table IV. Note that the coded values for some of the factors are not at a
full ±2 as might be expected. The augmented experimental runs showed that if the limits for some of the factors were extended
to two full experimental units, the resulting tablet would not have a measurable response. Modifications to the lower limits
had to be made to produce valid data for subsequent analysis. The repercussions of not using the two full experimental units
are that the standard error of prediction are no longer symmetrical throughout the design space.
Table IV: Response surface method: augmented central composite design.