Evaluation of the Poisson distribution for estimating the quality of drug/diluent random powder mixtures. I. High particle size of the drug constituent.

Use of the Poisson distribution to estimate the quality of random mixtures was evaluated as a measure of the highest attainable degree of dose uniformity of tablets. Ingredient A was assumed to have a large particle size as compared to diluent B. In contrast to the more precise binomial distribution, for the simple Poisson approach no experiments are necessary to investigate the mean proportions of the apparent volume, av and bv, which A and B assume within the powder samples in the die. The range of volume ratios was defined where the Poisson distribution is valid. Accepting an error of 5% of the random content variation of A per sample, av may amount to up to 0.1 (10%). In terms of the proportion by mass of A, a, this range is wider, and commonly of the order of 0.2 or higher. This approach was tested with tablets prepared from mixtures of coarse sucrose A and a fine Avicel/talc diluent B at A:B (m:m) ratios from 10:90 to 50:50. Even with the 30:70 tablets, the variations of the sucrose content were still in good agreement with the content variations of the random mixtures as estimated from the Poisson distribution. Estimates of the 50:50 ratio, however, deviated from the Poisson distribution.