A spatial rank-based multivariate EWMA control chart

Nonparametric control charts are useful in statistical process control (SPC) when there is a lack of or limited knowledge about the underlying process distribution, especially when the process measurement is multivariate. This paper develops a new multivariate self-starting methodology for monitoring location parameters. It is based on adapting the multivariate spatial rank to on-line sequential monitoring. The weighted version of the rank-based test is used to formulate the charting statistic by incorporating the exponentially weighted moving average control (EWMA) scheme. It is robust to non-normal data, easy to construct, fast to compute and also very efficient in detecting multivariate process shifts, especially for small or moderate shifts when the process distribution is heavy-tailed or skewed. As it avoids the need for a lengthy data-gathering step before charting and it does not require knowledge of the underlying distribution, the proposed control chart is particularly useful in start-up or short-run situations. A real-data example from white wine production processes shows that it performs quite well in the real application.