Moving blocks bootstrap control chart for dependent multivariate data

A method for constructing moving blocks bootstrap control chart for dependent multivariate data was proposed. In this method the statistics of the control charts were firstly obtained by principal component analysis, then a modified MBB was used to determine their control limits which can not be based on independent and identically distributed (IID) assumption. Empirical average run length and false alarm rate were proposed to evaluate the control charts. Two examples, adopting simulation data and real industrial data respectively, were given to illustrate the method, in which some results about factors' impact on MBB, such as sample size , moving block size, block number, et al., were obtained. The results show MBB-based method is superior to PCA-based method under certain conditions and is an available way to establish control charts for weakly dependent multivariate data.