An affine invariant signed-rank multivariate exponentially weighted moving average control chart for process location monitoring

Multivariate statistical process control (SPC) charts for detecting possible shifts in mean vectors assume that data observation vectors follow a multivariate normal distribution. This assumption is ideal and seldom met. Nonparametric SPC charts have increasingly become viable alternatives to parametric counterparts in detecting process shifts when the underlying process output distribution is unknown, specifically when the process measurement is multivariate. This study examined a new nonparametric signed-rank multivariate exponentially weighted moving average type (SRMEWMA) control chart for monitoring location parameters. The control chart was based on adapting a multivariate spatial signed-rank test. The test was affine-invariant and the weighted version of this test was used to formulate the charting statistic by incorporating the exponentially weighted moving average (EWMA) scheme. The test's in-control (IC) run length distribution was examined and the IC control limits were established for different multivariate distributions, both elliptically symmetrical and skewed. The average run length (ARL) performance of the scheme was computed using Monte Carlo simulation for select combinations of smoothing parameter, shift, and number of p-variate quality characteristics. The ARL performance was compared to the performance of the multivariate exponentially weighted moving average (MEWMA) and Hotelling T2. The control charts for observation vectors sampled the multivariate normal, multivariate t, and multivariate gamma distributions. The SRMEWMA control chart was applied to a real dataset example from aluminum smelter manufacturing that showed the SRMEWMA performed well. The newly investigated nonparametric multivariate SPC control chart for monitoring location parameters---the Signed-Rank Multivariate Exponentially Weighted Moving Average (SRMEWMA)---is a viable alternative control chart to the parametric MEWMA control chart and is sensitive to small shifts in the process location parameter. The signed-rank multivariate exponentially weighted moving average performance for data from elliptically symmetrical distributions is similar to that of the MEWMA parametric chart; however, SRMEWMA's performance is superior to the performance of the MEWMA and Hotelling's T2 control charts for data from skewed distributions.