A Design of Experiments for Tablet Compression - Pharmaceutical Technology

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A Design of Experiments for Tablet Compression
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 Pharmaceutical Technology Volume 35, Issue 9

Analysis of experimental design

 Figure 1: Half-normal plot of tablet hardness.
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, R 2 is 0.9881, adjusted R 2 is 0.9842, and adequate precision is 56.625. The R 2 of 0.9881 is in reasonable agreement with the adjusted R 2 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 outliers.

 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 analysis.

 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.

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