Robust Multivariate Control Charts

Most of the manufacturing, business and service processes depend on multiple related characteristics which face two types of variations primarily due to common or special causes. Common causes are part of every process, these are unavoidable and harmlessness. On the other hand, special causes appear in the process due to some associated problems that require special attention to address them. These special causes introduce a shift in the process. Statistical process control (SPC) tools are very famous in detecting these shifts. Control chart is one of the tools of SPC to handle the aforementioned matter. The control charts are categorized as memory and memoryless. Memory-less control charts commonly known as Shewhart (X-bar, R and S) charts are efficient to detect the large amount shifts. In contrary, the memory control charts such as cumulative sum (CUSUM) and exponentially weighted moving (EWMA) chart are effective in detecting the medium/small size shifts. The classical MEWMA control chart for monitoring a multivariate process is often based on estimated parameters from an in-control historical data. However, the data set may contain outliers or contaminated samples that could affect the accuracy of the estimates and subsequently have adverse effect on the performance of the control chart. In this article, we study the estimation methods for the location parameters: the mean, median, Hodges-Lehmann and trimean, under normal and contaminated environments. Using simulations, we studied the impact of the estimators on the performance of the MEWMA control chart in terms of the average run length. A numerical example is also given to illustrative implementation real-life data set.