A generalized exponentially weighted moving average control chart for monitoring autocorrelated vectors

Abstract

With recent advancement in automation and data acquisition technologies, a number of quality variables are often measured at high frequency and thus are likely to be autocorrelated. The multivariate exponentially weighted moving average (MEWMA) control chart with a scalar smoothing parameter has been widely suggested for monitoring autocorrelated vectors, owing to its simplicity. However, the use of a scalar smoothing parameter cannot take the correlation structure of variables into account, which in turn could deteriorate the detection performance of MEWMA control charts. Motivated by this, we generalize the MEWMA chart for monitoring autocorrelated vectors by using a weight matrix instead of a scalar smoothing parameter. The weight matrix is expected to have non-zero off-diagonal elements in order to make use of the correlation structure of the variables. The comparison results show that the generalized MEWMA chart can outperform the traditional MEWMA chart under a majority of shift directions, although it complicates the chart design to some extent.

Keywords:

• Average run length
• Full smoothing matrix
• Vector autocorrelated processes

Acknowledgements

The authors are very grateful to the Editor and anonymous referees for their valuable comments.

Additional information

Funding

Dr. Binhui Wang’s work was supported by the National Social Science Foundation of China (16BTJ035). Dr. Lianjie Shu’s work was supported in part by the Research Committee under the grant MYRG2018-00087-FBA, and the Science and Technology Development Fund, Macau SAR (FDCT0064/2018/A2 and FDCT0033/2020/A1).