Anomaly Detection for Compositional Data using VSI MEWMA control chart

In recent years, the monitoring of compositional data using control charts has been investigated in the Statistical Process Control field. In this study, we will design a Phase II Multivariate Exponentially Weighted Moving Average (MEWMA) control chart with variable sampling intervals to monitor compositional data based on isometric log-ratio transformation. The Average Time to Signal will be computed based on the Markov chain approach to investigate the performance of the proposed chart. We also propose an optimization procedure to obtain the optimal control limit, smoothing constant, and out-of-control Average Time to Signal for different shift sizes and short sampling intervals. The performance of the proposed chart in comparison with the standard MEWMA chart for monitoring compositional data is also provided. Finally, we end the paper with a conclusion and some recommendations for future research.