Probabilistic analysis of weight variability in tablets & capsules arising from the filling of a cavity with powder of a poly-dispersed size

The filling of a cavity space with a powdered material to produce tablets, capsules or pellets is an important operation across a number of industries including pharmaceuticals, health-food supplements and animal feeds. Variability in the mass of the product must be controlled. The objective of this paper is to quantify the dispersion in the tablet mass as a result of non-uniformity in the amount of material deposited in the cavity by consideration of the basic statistics of the process. The system under analysis is where powder is poured into a cavity, allowed to overflow the cavity and the free surface swept horizontally. A statistical approach to the parameters that introduce variability into the system is adopted to quantify the resulting dispersion in weight. Theoretical expressions for the mean and variance in tablet mass are developed. It is shown that dispersion in tablet mass results from variability in powder size and in the number of particles deposited in the cavity together with the effects of random packing. The theory is validated using a model system of glass beads and then applied to a more realistic example of pharmaceutical particles. It is shown that as a result of this analysis there are approaches that can be used to reduce tablet weight dispersion.