A general multivariate exponentially weighted moving-average control chart

This paper proposes a general multivariate exponentially weighted moving-average (MEWMA) chart in which the smoothing matrix is full, rather than having only diagonal elements. The average run-length properties of this scheme are examined for a diverse set of quality-control environments. The performance of the scheme is measured by estimating the ARL and comparing it with that of the traditional diagonal multivariate EWMA chart. The comparison shows that allowing nonzero off-diagonal elements in the weight matrix of the new chart can improve MEWMA performance compared with the current standard of a diagonal weight matrix. In particular, there can be a substantial improvement when the process shifts out of control in the start-up stage. The performance of the chart is illustrated with some medical data. Univariate methods are far inferior to multivariate methods on this data set, and the full MEWMA chart proposed outperforms the diagonal MEWMA chart.