Directed monitoring using Cuscore charts for seasonal time series

The most commonly used statistical process control charts to detect special causes are Shewhart and Cusum charts. However, the Cuscore chart is a contemporary alternative that is especially well suited for detecting special causes that can be modeled in advance based on their characteristic effect on the system. In this paper, we develop the appropriate Cuscore statistic and the required control limits to detect a mean shift in a seasonal time series process. The work is motivated by an application involving blood platelet orders placed with the Red Cross. We also compare the performance of the Cuscore chart to the Cusum chart in this application and find that the performance of the Cuscore, in terms of time to signal the special cause, is better than the Cusum chart. We find that this result holds even when faced with the mismatch problem, which pertains to the compatibility between the actual and expected information that the Cuscore statistic is predicated on.