An Explanatory Study on the Non-Parametric Multivariate T2 Control Chart

Abstract

Most control charts require the assumption of normal distribution for observations. When distribution is not normal, one can use non-parametric control charts such as sign control chart. A deficiency of such control charts could be the loss of information due to replacing an observation with its sign or rank. Furthermore, because the chart statistics of T² are correlated, the T² chart is not a desire performance. Non-parametric bootstrap algorithm could help to calculate control chart parameters using the original observations while no assumption regarding the distribution is needed. In this paper, first, a bootstrap multivariate control chart is presented based on Hotelling’s T² statistic then the performance of the bootstrap multivariate control chart is compared to a Hotelling’s T² parametric multivariate control chart, a multivariate sign control chart, and a multivariate Wilcoxon control chart using a simulation study. Ultimately, the bootstrap multivariate control chart is used in an empirical example to study the process of sugar production.Non-parametric bootstrap, misspecified model, multivariate sign control
chart, multivariate Wilcoxon control chart, average run length