The author prepared and analyzed a detailed design of experiments for the manufacture of a simple tablet formulation. The aim was to test whether tablet hardness and weight could be controlled during the compression process by adjusting certain machine parameters.
Sep 2, 2011 By:
Matthew N. Bahr Pharmaceutical Technology
Hardness response. Two responses, tablet hardness and tablet weight, were measured throughout the set of experiments. Each measure response
was analyzed individually. Using Design-Expert software, a half-normal plot of the experimental data results was constructed
from the original screening results. The half-normal plot for the tablet hardness is shown in Figure 1. Only the significant
factors are identified in the half-normal plot. After the sample tablets were pulled from the rotary tablet press, the tablets
were left stationary for 2 min before being tested, according to the standard protocol, as previously described. During a
formal campaign, the finished batch may be held for at least 24 h before being sampled and tested again. The purpose of the
delay is to ensure that the tablets did not rebound because of the compressed material's elasticity. Elastic tablets tend
to expand after compression, thus causing a decrease in measured tablet hardness.
Table V: Analysis of variance for augmented central composite design model according to tablet hardness.
The half-normal plot indicates that factors A, C, D, and E, and interactions CD and CE significantly affected the hardness
response. The analysis of variance shown in Table V supports the plot in Figure 1.
In the next equation, R2
is 0.9881, adjusted R2
is 0.9842, and adequate precision is 56.625. The R2
of 0.9881 is in reasonable agreement with the adjusted R2
of 0.9842. The adequate precision ratio of 56.625 indicates an adequate signal, so the following model, in terms of coded
factors, can be used to establish the design space:
Figure 2: Normal plot of residuals for hardness.
The 95% confidence intervals for all significant factors were verified to exclude zero, which supports the determination that
all identified terms in the model equation influence the response. A normal plot of residuals was constructed to determine
whether residuals followed a normal distribution (see Figure 2). A plot of residuals versus predicted was constructed to discover
convincing trends to the residuals or suspected outliers in the data (see Figure 3). All data points are equally distributed
and are within two standard deviations from the mean with two exceptions: one high point is 2.206 standard devations, and
one low point is –2.312 standard deviations. The two data points that lie beyond two standard deviations of the mean could
be investigated, and these experiments may warrant being rerun to confirm the data response. The data showed no potential
Figure 3: Residuals versus predicted plot for hardness.
Appendix Figure 1: Hardness interaction plot for precompression and main compression.
Plots were generated for the interactions of CD and CE. These plots are included in the appendix of supporting figures. The
3D-contour CD interaction plot is shaped like a spade because of the data collected during the centerpoint experimental runs.
The interaction plot shows that tablet hardness increased as main compression and precompression heights were reduced (see
Appendix Figures 1 and 2). This makes logical sense because when the compression rollers are pulled close together, high compression
forces are imposed on the tablet, thus resulting in hard tablets. Both 3D plots and standard interaction plots support this
Appendix Figure 2: Hardness 3D interaction plot for precompression and main compression.
Appendix Figure 3: Hardness interaction plot for precompression and fill-cam height.
The 3D contour CE interaction plot shows a response similar in shape to that of the CD interaction plot, but the shape is
more easily interpreted as a channel (i.e., an inverted ridge with a slope that has not yet reached its minimum). The CE interaction
plot (see Appendix Figures 3 and 4) indicates an increase in hardness when the fill-cam height (i.e., factor E) is low or
high and the precompression roller height is reduced (thus increasing compression force), as would be expected. The tablet
weight responded linearly as the fill-cam height (i.e., the weight-adjustment ramp) changed.
Appendix Figure 4: Hardness 3D interaction plot for precompression and fill-cam height.