Self-oriented control charts for efficient monitoring of mean vectors

• We successfully monitor mean vectors maximising the trace between two populations.
• Don’t need to select the direction that optimises the process change.
• The proposed charts are as simple to apply as the MEWMA and CUSUM charts.
• The control charts showed less inertia than the quadratic approaches.

This work presents a procedure for monitoring the centre of multivariate processes by optimising the noncentrality parameter with respect to the maximum separability between the in- and out-of-control states. Similarly to the Principal Component Analysis, this procedure is a linear transformation but using a different criterion which maximises the trace of two scatter matrices. The proposed linear statistic is self-oriented in the sense that no prior information is given, then it is monitored by two types of control charts aiming to identify small and intermediate shifts. As the control charts performances depend only on the noncentrality parameter, comparisons are made with traditional quadratic approaches, such as the Multivariate Cumulative Sum (MCUSUM), the Multivariate Exponentially Weighted Moving Average (MEWMA) and Hotelling’s T2 control chart. The results show that the proposed statistic is a solution for the problem of finding directions to be monitored without the need of selecting eigenvectors, maximising efficiency with respect to the average run length.