A CUSUM scheme for event monitoring

Abstract

This article presents a single CUSUM scheme (called the GCUSUM chart) for simultaneously monitoring the time interval T and magnitude X of an event. For example, a traffic accident may be considered as an event, and the total loss in dollars in each case is the event magnitude. Since the GCUSUM chart is developed based on a synthetic statistic G which is a function of both T and X, this new chart is able to make use of the information about the event frequency, as well as the information about the event magnitude. Moreover, the detection power of the GCUSUM chart can be allocated in an optimal manner between those against T shifts and against X shifts, and between those against small shifts and against large shifts. The performance studies show that the GCUSUM chart is more effective than all other charts in the current literature for detecting the out-of-control status of an event. Furthermore, the GCUSUM chart performs more uniformly for detecting process shifts of different types and sizes. This chart is also easier to be designed and implemented than other CUSUM charts for monitoring both T and X. The GCUSUM chart has the potential to be applied to many different areas, especially to the non-manufacturing and service sectors, such as supply chain management, homeland security, office administration and the health care industry.