To propose a general multivariate exponentially weighted moving average (MEWMA) chart in which the smoothing matrix is full, rather than having only diagonal elements. The standard Shewhart charts provide good performance in detecting large changes in a process, but are much less effective for smaller but persistent changes. Lowry, et al. (Ref. 1) extended the original univariate EWMA procedure to a multivariate control chart scheme for controlling the mean vector of a multivariate normal process. Their multivariate EWMA (MEWMA) chart is a straightforward vector generalization of the corresponding univariate procedure, using a smoothing matrix instead of the scalar smoothing constant of the EWMA. Current MEWMA practice seems to be confined to using a smoothing matrix with zero off-diagonal elements and generally equal diagonal elements, Lowey, et al. (Ref. 1), though Yumin (Ref. 2) showed the potential benefits of unequal diagonal elements. The authors will use the abbreviation DEWMA for this standard MEWMA with equal nonzero elements on the diagonal of the smoothing matrix and zeroes off the diagonal. A general MEWMA chart with an unrestricted smoothing matrix is proposed in this paper. The authors will use the abbreviation of FEWMA for the multivariate EWMA chart with a full smoothing matrix.
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