Benneyan Test
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Smaller values on a G chart indicate fewer days between events or fewer opportunities between events. When 0 is plotted on a G chart, events either occurred on the same day or events occurred in consecutive order.

To detect high rates of an event, Minitab performs the Benneyan Test. The lower control limit for a G chart is 0 in most cases. Also, the minimum data value is 0, which means that you cannot detect when the rate of rare events is unusually high by observing which points are below the lower control limit.

The Benneyan test counts the number of consecutive plotted points equal to 0. When a point on a G chart fails the Benneyan test, the point is marked with B. The number of points that are required to signal the Benneyan Test is a function of the desired false alarm rate and the event probability. The false alarm rate is based on the probability that is associated with the test 1 argument, which is 3 by default.

See [3] for more discussion about the Benneyan Test.