A class of nonparametric Max-EWMA schemes for monitoring high-dimensional processes

This paper introduces a class of Max-type nonparametric exponentially weighted moving average (Max-EWMA) schemes for high-dimensional processes based on interpoint and various Minkowski distances. The Max-EWMA monitoring scheme uses a plotting statistic based on the maximum of the absolute values of two EWMA statistics based on rank scores, one for the location and the other for the scale aspects of the distance distribution, equivalent to operating two EWMA schemes with standard control limits. The advantages of the Max-EWMA-type schemes over some existing high-dimensional Phase-II monitoring schemes are investigated. More specifically, several Monte Carlo simulations are conducted. The main conclusions are that the proposed Max-EWMA schemes exhibit robust in-control (IC) performance across different continuous multivariate distributions and, in the out-of-control (OOC) case, no distance metric completely outperforms the others. The Manhattan distance seems preferable when there are linear location shifts across all variables. In some sparse location-shift settings, Euclidean distance performs better for linear location shifts in an asymmetric multivariate population. In contrast, Chebyshev’s distance performs better for a couple of symmetric multivariate densities. Finally, the implementation of the schemes is shown by monitoring production process data from a semiconductor manufacturing process.