  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 proposed chart. We also propose an optimal 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 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.
