Monitoring shift on non-normal multivariate processes using T ²hotelling double Bootstrap control chart

This study aims to find a sensitive control chart to monitor shifts in data with a multivariate non-normal distribution using T2 Hotelling. However, the normal multivariate assumption in the T2 Hotelling control chart is a problem. So that in this study, the Double Bootstrap method was developed to determine the control limits on the T^2 Hotelling control chart. Double Bootstrap is a development of the Bootstrap method with the advantage that it is effective in determining control charts when process control is skewed. The performance of the proposed control chart is tested using simulation data with a multivariate exponential distribution. The magnitude of the shift is also given from a small shift (δ=0.001) to a large shift (δ=3.0) with a false alarm probability of α= 0.05. Then through the Average Run Length (ARL) the sensitivity of the proposed T2 Double Bootstrap control chart is compared with the single bootstrap control chart. The result shows that the Double Bootstrap control limit on the non-normal multivariate processes is more sensitive for all shifts than the Single Bootstrap. Thus, the proposed control chart is not only good at detecting shifts but also provides a way to minimize errors in multivariate process control.