A nonparametric multivariate cumulative sum procedure for detecting shifts in all directions

Summary. The fairly limited range of tools for multivariate statistical process control generally rests on the assumption that the data vectors follow a multivariate normal distribution—an assumption that is rarely satisfied. We discuss detecting possible shifts in the mean vector of a multivariate measurement of a statistical process when the multivariate distribution of the measurement is non-Gaussian. A nonparametric cumulative sum procedure is suggested which is based both on the order information among the measurement components and on the order information between the measurement components and their in-control means. It is shown that this procedure is effective in detecting a wide range of possible shifts. Several numerical examples are presented to evaluate its performance. This procedure is also applied to a data set from an aluminium smelter.