Individual T₂ control chart for compositional data

The usual Hotelling T₂ control chart is not appropriate for monitoring processes where the quality characteristic is a mixture. The composition of mixtures are vectors of positive elements that represent parts of a whole, to which standard multivariate techniques are not appropriate due to their restricted sample space. There are many applications where a mixture is monitored against time, such as in the chemical industry, product composition, impurity profile, or gas components analysis. In this paper, a multivariate control chart for individual compositional observations based on the T₂ statistic is proposed and compared with the typical one in terms of average run length. We show how results are more consistent with compositional data nature and illustrate implementation in a real-world example.