A CUSUM scheme for monitoring the frequency and magnitude of a negative event

This article proposes a Cumulative Sum (CUSUM) scheme, called the TX-CUSUM scheme, for the monitoring of a negative event. It is able to check both the time interval (T) between occurrences of the event and the magnitude (X) of each occurrence. In this article, T is assumed to follow an exponential distribution and X is assumed to follow a gamma distribution. Our studies show that the TX-CUSUM scheme is much more effective than the existing Shewhart-type T&X chart for monitoring, so that cost or loss incurred by an event can be reduced by using this scheme. The improvement in performance is achieved because of the use of the CUSUM feature and the simultaneous monitoring of T and X.