The purpose of this article is to summarize recent research results for constructing nonparametric multivariate control charts with main focus on data depth based control charts. Data depth provides data reduction to large-variable problems in a completely nonparametric way. Several depth measures including Tukey depth are shown to be particularly effective for purposes of statistical process control in case that the data deviates normality assumption. For detecting slow or moderate shifts in the process target mean, the multivariate version of the EWMA is generally robust to non-normal data, so that nonparametric alternatives may be less often required.
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The definitive version is available at: http://onlinelibrary.wiley.com/doi/10.1002/asmb.2186/full
Bae, Suk Joo, Giang Do, and Paul Kvam. "On Data Depth and the Application of Nonparametric Multivariate Statistical Process Control Charts." Applied Stochastic Models in Business and Industry 32, no. 5 (2016): 660-76. doi:10.1002/asmb.2186.
Bae, Suk Joo; Do, Giang; and Kvam, Paul, "On Data Depth and the Application of Nonparametric Multivariate Statistical Process Control Charts" (2016). Math and Computer Science Faculty Publications. 168.