Directionally sensitive multivariate control charts in practice: Application to biosurveillance

Multivariate control charts are used for monitoring multiple series simultaneously, for the purpose of detecting shifts in the mean vector in any direction. In the context of disease outbreak detection, interest is in detecting only an increase in the process means. Two practical approaches for deriving directional Hotelling charts are Follmann's correction and Testik and Runger's quadratic programming. However, there has not been an extensive comparison of their practical performance. Moreover, in practice, many of the underlying method assumptions are often violated, and the theoretically guaranteed performance might not hold. In this work, we compare the two directionally sensitive approaches: a statistically based approach and an operations research solution. We evaluate Hotelling charts as well as two extensions to multivariate exponentially weighted moving average charts. We examine practical performance aspects such as robustness to often-impractical assumptions, the amount of data required for proper performance, and computational aspects. We perform a large simulation study and examine performance on authentic biosurveillance data.