Computation of average run length for residual-based T 2 control chart for multivariate autocorrelated processes

The expression of residual is obtained according to its dynamic response to mean shift,then the distribution of T 2 statistic applied to the residual is derived,thus the probability of the T 2 statistic lying outside the control limit is calculated.The above-mentioned results are substituted into the infinite definition expression of the average run length(ARL),and then the final finite ARL expression is obtained.An example is used to demonstrate the procedures of the proposed method.In the comparative study,eight autocorrelated processes and four different mean shifts are performed,and the ARL values of the proposed method are compared with those obtained by simulation method with 50,000 replications.The accuracy of the proposed method can be illustrated through the comparative results.