Simultaneous monitoring of multivariate time between events and their magnitude using multivariate marked Hawkes point process

Abstract

In this paper, monitoring the time between events is discussed. The control chart of the time between events in multivariate mode discusses the conditions under which the Hawkes point process generates the time data. It is also necessary to consider that monitoring time data individually and regardless of the magnitude of an event is not very important. Therefore, in addition to monitoring time data, it is also essential to monitor the magnitude of an event. Because of that, the magnitude of each event is considered along with monitoring the time between multivariate events through data generation with the multivariate marked Hawkes point process. Three statistics are presented for simultaneous monitoring of the time between events and the magnitude. A Max-EWMA, two single EWMA that each of which are used to monitor TBE and magnitude (TSEWMA), and the third statistic, derived from existing literature, is a Shewhart statistic that has been integrated into an EWMA statistic framework (EWMA-Z). These charts have been used for a case study and compared according to different shifts.

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