Generalized smoothing parameters of a multivariate EWMA control chart

The Multivariate Exponentially Weighted Moving Average (MEWMA) control chart is effective in detecting a small process mean shift. Its simplicity and generality stem from the assumption that the smoothing parameters of the variables are given constants and equally distributed on the diagonal of the smoothing matrix. Recently, the MEWMA model with the full non-diagonal smoothing matrix (FEWMA) is studied. The model, however, has limited use due to the assumption that the off-diagonal elements are the same; therefore, it would necessarily be sensitive to the correlation structure of observations. In this article, we propose a generalized model for the MEWMA, that uses appropriate non-diagonal elements in the smoothing matrix based on the correlation among variables. We also offer an interpretation of off-diagonal elements of the smoothing matrix and suggest an optimal design for a proposed MEWMA chart. A case study on the automatic monitoring of dimensions of bolts using an imaging processing system is presented to illustrate the proposed control chart. The proposed model is effective in detecting small mean shifts and shows improved performance when compared with MEWMA, FEWMA, and other recently improved control charts.