Monitoring the frequency and magnitude of an event with a ratio chart

Control charts for monitoring the event has attracted many researchers´ interests and many works have been done in recent years. However, previous works always neglect the dependence between event frequency and event magnitude and this kind of ignorance may make the control chart not suitable in some real applications. In our work, the frequency and magnitude of an event is characterized by a bivariate gamma distribution with a dependence parameter. And the ratio of the event magnitude and event frequency is introduced and the EWMA type of the ratio is considered as the monitoring statistic. The implementation procedure of the introduced chart is discussed with an example.