Phase II monitoring of general linear profiles in the presence of between-profile autocorrelation

In this paper, an approach based on the U statistic is first proposed to eliminate the effect of between profile autocorrelation of error terms in Phase-II monitoring of general linear profiles. Then, a control chart based on the adjusted parameter estimates is designed to monitor the parameters of the model. The performance of the proposed method is compared with the ones of some existing methods in terms of average run length for weak, moderate, and strong autocorrelation coefficients under different shift scenarios. The results show that the proposed method provides significantly better results than the competing methods to detect shifts in the regression parameters while the competing methods perform better in detecting shifts in the standard deviation. At the end, the applicability of the proposed method is illustrated by an example.