An integrated T and TCUSUM scheme

This article proposes an integrated scheme (T&TCUSUM chart) which combines a Shewhart T chart and a TCUSUM chart (a CUSUM-type T chart) to monitor the time interval T between the occurrences of an event or the time between events (TBE). The performance studies show that the T&TCUSUM chart can effectively improve the overall performance over the entire T shift range. On average, it is more effective than the T chart by 26.66% and the TCUSUM chart by 14.12%. Moreover, the T&TCUSUM chart performs more uniformly than other charts for detecting both small and large T shifts, because it has the strength of both the T chart (more sensitive to large shifts) and the TCUSUM chart (more sensitive to small shifts). The implementation of the new chart is almost as easy as the operation of a TCUSUM chart.