Monitoring counting processes has gone unchallenged for some time and process monitoring the frequency of events has become the standard for the early detection of the outbreak of events. Examples of event outbreaks are disease outbreaks, sales unexpected growth, species abundance monitoring, fish stock, warrantee claims on a product, etc. Monitoring event counts over time needs to select a time window over which these events are counted and this is a form of temporal aggregation. In these counting processes any increase in the events can only be assessed at the end of each time period. This is a disadvantage when monitoring event outbreaks because it does not provide real-time evidence that the frequency of events are increasing.
The time between these events (TBE) on the other hand does provide real-time information on outbreaks because the timing of the event contains all the information needed to monitor event outbreaks in real-time. An alternative often considered in these cases is to take the intervals as small as possible so that events within intervals are rare and monitor using Bernoulli sequences. This does improve the real-time assessment of outbreaks but when e