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.


Pharmaceutical Technology
Volume 35, Issue 9


Table III: Analysis of variance for factorial model according to tablet weight.
A response ratio of 11.8485 suggests that the model should be transformed. After detailed analysis of the optional transformations, a square-root transformation appeared to present results with the highest confidence.

The model F value of 509.46 implies that the model was significant. The chance that a model F value this large could occur as a result of noise is less than 0.01%.

Values of p > F less than 0.0500 (at a 95% confidence interval) indicate that model terms were significant. In this case A, C, D, E, CD, and CE are significant model terms (see Table I).

The curvature F value of 109.91 implies that curvature in the design space, as measured by the difference between the average of the center points and the average of the factorial points, was significant. The chance that a curvature F value this large could occur as a result of noise is only 0.01%.

The lack-of-fit F value of 1.74 implies that the lack of fit was not significant relative to pure error, and this result is desirable. The chance that a lack-of-fit F value this large could occur as a result of noise is 41.83%.

The software produces equations that show how the hardness will respond when any of the factors in the equation change. R 2 measures the confidence that the hardness will be what is expected. Adjusted R 2 takes into account the variances of the errors. For the first equation, R 2 is 0.9964, adjusted R 2 is 0.9945, and adequate precision is 70.834.

The R 2 of 0.9964 is in reasonable agreement with the adjusted R 2 of 0.9945. Adequate precision measures the signal-to-noise ratio. A ratio greater than 4 is desirable. The ratio of 70.834 indicates an adequate signal. The following model equation, in terms of coded factors, can be used to establish the design space:




The model F value of 999.17 implies the model was significant. The chance that a model F value this large could occur as a result of noise is less than 0.01%.

Values of prob >F less than 0.0500 indicate that the model terms were significant. In this experiment, A, B, C, and E were significant model terms.

The curvature F value of 1.16 implies the absence of curvature. The chance that a curvature F value this large could occur as a result of noise is 30.09% .

The lack-of-fit F value of 2.17 implies that the lack of fit was not significant relative to pure error, and this result is desirable. The chance that a lack-of-fit F value this large could occur as a result of noise is 35.76%.

For the second equation, R 2 is 0.9968, adjusted R 2 is 0.9958, and adequate precision is 70.577. The R 2 of 0.9968 is in reasonable agreement with the adjusted R 2 of 0.9958. The adequate precision ratio of 70.577 indicates an adequate signal. The following equation, in terms of coded factors, can be used to establish the design space:





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