A Multivariate Sign EWMA Control Chart

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 elliptical direction class, the IC average run length can be calculated via a one-dimensional Markov chain model. This control chart possesses some other favorable features: it is fast to compute with a similar computational effort to the MEWMA chart; it is easy to implement because only the multivariate median and the associated transformation matrix need to be specified (estimated) from the historical data before monitoring; it is also very efficient in detecting process shifts, particularly small or moderate shifts when the process distribution is heavy tailed or skewed. Two real-data examples from manufacturing show that it performs quite well in applications. This article has supplementary material online.