Periodic Cuscore charts to detect step shifts in autocorrelated processes

Among statistical control charts, the Cuscore control chart has been designed specifically for particular types of signals and process models. The synchronization between the residuals of the process and the detectors of the Cuscore makes this control chart more sensitive for detecting a signal than the Shewhart, cusum and other standard control charts. However, this synchronization happens only when the time of the occurrence of the signal is known. In this paper, we develop two approaches for applying the Cuscore chart when the time of the signal is unknown. The first approach is to reinitialize the Cuscore statistic with a prescribed cycle. The second approach considers only the most recent time periods to calculate the Cuscore statistic. We apply these two approaches to construct what we call periodic Cuscore control charts to detect step shifts in seasonal time series processes. Simulation results show that the performance of periodic Cuscore charts, in terms of average run length to signal a special cause, is better than that of cusum charts in most cases even when faced with a long mismatch period between the time of resetting the charts and the time of the occurrence of the signal. These results indicate that the two approaches are practical and effective when the time of the signal is unknown.