A Multivariate Sign EWMA Control Chart.

TLDR: A new multivariate SPC methodology for monitoring location parameters is developed based on adapting a powerful multivariate sign test to online sequential monitoring, which results in a nonparametric counterpart of the classical multivariate EWMA (MEWMA).

Abstract: Nonparametric control charts are useful in statistical process control (SPC) when there is a lack of or limited knowledge about the underlying process distribution, especially when the process measurement is multivariate. This article develops a new multivariate SPC methodology for monitoring location parameters. It is based on adapting a powerful multivariate sign test to online sequential monitoring. The weighted version of the sign test is used to formulate the charting statistic by incorporating the exponentially weighted moving average control (EWMA) scheme, which results in a nonparametric counterpart of the classical multivariate EWMA (MEWMA). It is affine-invariant and has a strictly distribution-free property over a broad class of population models. That is, the in-control (IC) run length distribution can attain (or is always very close to) the nominal one when using the same control limit designed for a multivariate normal distribution. Moreover, when the process distribution comes from the elli...