摘要
The expression of residual is obtained according to its dynamic response to mean shift, then the distribu- tion of T2 statistic applied to the residual is derived, thus the probability of the 7a 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.
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.
基金
Supported by National Natural Science Foundation of China (No.70931004 and No. 70802043)
