Bootstrap-based T² multivariate control charts

Control charts have been used effectively for years to monitor processes and detect abnormal behaviors. However, most control charts require a specific distribution to establish their control limits. The bootstrap method is a nonparametric technique that does not rely on the assumption of a parametric distribution of the observed data. Although the bootstrap technique has been used to develop univariate control charts to monitor a single process, no effort has been made to integrate the effectiveness of the bootstrap technique with multivariate control charts. In the present study, we propose a bootstrap-based multivariate T² control chart that can efficiently monitor a process when the distribution of observed data is nonnormal or unknown. A simulation study was conducted to evaluate the performance of the proposed control chart and compare it with a traditional Hotelling's T₂ control chart and the kernel density estimation (KDE)-based T₂ control chart. The results showed that the proposed chart performed better than the traditional T₂ control chart and performed comparably with the KDE-based T ₂ control chart. Furthermore, we present a case study to demonstrate the applicability of the proposed control chart to real situations.