Shrinkage estimates of covariance matrices to improve the performance of multivariate cumulative sum control charts

Multivariate cumulative sum control charts require knowledge of the in-control process covariance parameters. Here, we show that the performance of the multivariate cumulative sum control charts for individual-observation monitoring is affected by the estimation of parameters unless the Phase I sample size is large. When only a small Phase I sample size is available, we propose the use of a shrinkage estimate. The average run length performance of multivariate cumulative sum control charts obtained using the shrinkage estimate is superior to the other methods examined in this study. The improved performance of the control charts using the shrinkage estimate is also demonstrated via an illustrative case study of Bimetal data, in which measurements of four properties of bimetal brass and steel thermostats are monitored, and a shift in the multivariate centroid is detected earlier using the shrinkage-based method.