A note Computation of Multivariate Control Limits: The Bootstrap Approach

This work focuses on how to set control limits that will best identify signals in multivariate control charts. In any production process, every product is aimed to attain a certain standard, but the presence of assignable cause of variability affects our process thereby leading to low quality of product. However, the problem involved in the use of multivariate control chart is the violation of multivariate normal assumption. The first method develops bootstrap procedures to determine Hotelling's \(T^{2}\) control limits for detecting large shift. The second method develops bootstrap procedures for obtaining Multivariate Exponentially-Weighted Moving Average (BMEWMA) control limits for identifying small shift. Results from a performance study shows that the proposed methods enable the setting of control limits that can enhance the detection of out of control signals.