One Hotelling T2 chart based on transformed data for simultaneous monitoring the frequency and magnitude of an event

Commonly, the event frequency and event magnitude have the dependence feature. However, previous research about event monitoring always assume they are independent variables. This assumption is not reasonable in most real applications. Taken the dependence feature into consideration, we introduce a typical bivariate gamma distribution with certain dependence structure. Based on this distribution, a kind of Hotelling T² chart based on the transformed data is constructed for jointly monitoring of the shifts in the frequency and the magnitude of an event. An illustrative example based on a real data is provided to show the implementation of this chart. With Monte Carlo simulation, the performance of this proposed chart is studied.