PRACTICAL DECOMPOSITION METHOD FOR T2 HOTELLING CHART

Manuel Roman Piña-Monarrez

Abstract


In multivariate control process, the T2 Hotelling chart is the most useful, unfortunately, until now there was not an efficient decomposition method when the chart signals. The MTY method (Mason, Tracy and Young) is the most used method, but unfortunately it does not present a not unique decomposition and it is complex when there are many variables. In particular the estimated Mahalanobis distance (MD) and its decomposition for an out of control signal, not hold. In this article, by considering the inverse of the covariance matrix of phase I as a standard one, a practical decomposition method based on the relations of each pair of variables in this inverse matrix, is proposed. Results of its application show that the decomposition holds with the estimated MD, and that, let us to separate the contribution of each individual variable; in contribution due the variance and contribution due the correlation.


Keywords


Decomposition method, T2 Hotelling chart, Mahalanobis distance, Multivariate control

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