Design of MEWMA control chart for phase II monitoring Dirichlet-distributed compositional data

{Simulation is used to demonstrate a significant improvement in monitoring Dirichlet-distributed compositional data.} Compositional data comprise nonnegative multivariate values that sum to a constant, such as proportions or percentages. To handle the constraint of summing to a constant, the existing control charts for monitoring compositional data begin by applying a transformation, which is then used to develop the monitoring scheme. However, this approach hinders the interpretation of out-of-control signals. In this paper, we assume that compositional data follow the Dirichlet distribution and propose a multivariate exponentially weighted moving average (MEWMA) control chart for Phase II monitoring compositional process data. The proposed MEWMA chart can be used to directly monitor compositional data, simplifying both its implementation and the interpretation of out-of-control signals. The performance of the proposed chart is assessed through simulations and compared with the isometric log-ratio transformation methods in the literature. The proposed chart is also applied in a numerical example for an industrial plant in Europe to demonstrate its implementation.