Distribution-Free Multivariate Phase I Shewhart Control Charts: Analysis, Comparisons and Recommendations

The need to develop nonparametric techniques for multivariate Phase I analysis has received increasing attention in the statistical process monitoring literature. Some critical issues related to univariate Phase I analysis become even more challenging when several quality characteristics need to be analysed simultaneously. Multivariate Shewhart-type control charts, such as Hotelling’s control chart, are simple to use and effective in detecting large outliers in Phase I applications. However, the traditional design of the chart assumes that the underlying process distribution is multivariate normal. When this assumption is violated, the chart’s signals become questionable. This study investigates a class of distribution-free Phase I Shewhart-type control charts for detecting shifts in the location vector of a multivariate process. This class contains the original Hotelling’s control statistic, as well as other -type control statistics based on affine invariant transformations of the original multivariate data, such as the ranks of the Mahalanobis depths, the spatial signs and the multivariate spatial and signed ranks. To attain the desired in-control properties independently of the underlying process distribution, a permutation-based approach is used and recommended to compute the control limits. A simulation study is carried out to investigate the out-of-control performance of these distribution-free Phase I Shewhart control charts and provide practical recommendations to users.