Self-starting multivariate control charts for location and scale

Multivariate control charts are advisable when monitoring several correlated characteristics. The multivariate exponentially weighted moving average (MEWMA) is ideal for monitoring the mean vector, and the multivariate exponentially weighted moving covariance matrix (MEWMC) detects changes in the covariance matrix. Both charts were established under the assumption that the parameters are known a priori. This is seldom the case, and Phase I data sets are commonly used to estimate the chart's in-control parameter values. Plugging in parameter estimates, however, fundamentally changes the run-length distribution from those assumed in the known-parameter theory and diminishes chart performance, even for large calibration samples. Self-starting methods, which correctly studentize the incoming stream of process readings, provide exact control right from start up. We extend the existing multivariate self-starting methodology to a combination chart for both the mean vector and the covariance matrix. This approach is shown to have good performance.