Individual T-2 Control Chart for Compositional Data

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The usual Hotel ling T-2 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 T-2 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 ​
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