Monitoring compositional data using multivariate exponentially weighted moving average scheme

Recently, the monitoring of compositional data by means of control charts has been investigated in the statistical process control literature. In this article, we develop a Phase II multivariate exponentially weighted moving average control chart, for the continuous surveillance of compositional data based on a transformation into coordinate representation. We use a Markov chain approximation to determine the performance of the proposed multivariate control chart. The optimal multivariate exponentially weighted moving average smoothing constants, control limits, and out-of-control average run lengths have been computed for different combinations of the in-control average run lengths and the number of variables. Several tables are presented and enumerated to show the statistical performance of the proposed control chart. An example illustrates the use of this chart on an industrial problem from a plant in Europe.