A robust self-starting spatial rank multivariate EWMA chart based on forward variable selection

Shifts in one or a few components of process mean vectors, called sparse shifts, are monitored in many applications. To monitor sparse shifts, several control charts have recently been proposed based on the variable selection technique. These charts assume either that the in-control (IC) distribution is completely known or that a sufficiently large reference dataset is available. However, this assumption is not always valid in practice. This paper develops a self-starting control chart that integrates a multivariate spatial rank test with the EWMA charting scheme based on forward variable selection for monitoring sparse mean shifts. Both the theoretical and numerical results show that the proposed chart is robust to non-normally distributed data, fast to compute, easy to construct, and can efficiently detect sparse shifts, especially when the process distribution is heavy-tailed or skewed. The proposed control chart does not need prior knowledge of the IC distribution and can start monitoring even before considerable reference data have been collected. A real-data example from a white wine production process illustrates the effectiveness of the proposed control chart.