(120g) A Markov Chain Model for a Tablet Coating Process

A Markov chain is a mathematical model for a system undergoing random transitions from one state to another. The transition between states is described by a transition matrix and it is assumed that the transition depends only on the current state. In this work, a stationary Markov chain model is developed to model tablet coating in a rotating drum. Coating data from short Discrete Element Method (DEM) simulations are used to construct the transition matrix for the Markov process. The transition matrix is subsequently used to predict the inter-tablet coating variability at longer times. The predictions from the Markov chain model are then compared to those obtained directly from DEM. The effect of the time between transition states, number of states, and the learning time (time required to construct the transition matrix) for the Markov process are studied. It is found that the time between the transition states has a strong influence on the predicted inter-tablet coating variability. Good agreement with DEM is obtained when the transition time is chosen to be the time required for successive appearances of tablets in the spray zone, referred to as cycle time. The learning time should be large enough so that the transition matrix converges (as measured using an l₁-norm) and a transition into a state has at least one transition out of that state. The predictions get better as the number of states increases but also require a larger learning time.