A combined synthetic and generalized variance control chart for bivariate case

This study proposes a combined scheme, denoted as the combined syn-|S| control chart, which comprises a synthetic |S| sub-chart and a standard |S| sub-chart. This proposed control chart can be used to detect shifts in the covariance matrix of bivariate process (i.e. multivariate process with quality characteristics p = 2). It is assumed that the underlying process data follow a bivariate normal distribution. The design, performance and implementation of the combined syn-|S| control chart are provided. From the results of the performance comparison, it can be shown that the combined syn-|S| control chart performs better than the standard |S| control chart, the adaptive |S| control chart and the synthetic |S| control chart for monitoring process variability in terms of the average run length.