Select tests for special causes for G Chart

Stat > Control Charts > Rare Event Charts > G > G Chart Options > Tests

Minitab provides five tests for special causes. The G chart includes the Benneyan Test to detect high rates of a rare event. Experts recommend that you use both Test 1 and Test 2 when you create a G chart because the G chart may be slow to detect small to moderate decreases in the average number of days or number of opportunities between events. Select additional tests based on company or industry standards. Use the tests to determine which observations to investigate, and to identify the specific patterns and trends in your data.

For the traditional control charts for attribute data, Test 1 is based on the normal distribution. However, for G charts, Test 1 is based on the geometric distribution. A point on a G chart fails Test 1 when it is outside the percentiles of the geometric distribution that correspond to 3 standard deviations from the center line in a normal distribution. For more information, go to Methods and formulas for G chart and click "Tests for special causes, including Benneyan test".

In the drop-down list, specify whether to perform some, all, or no tests for special causes. You can make each test more or less sensitive by changing the value of K.

Tip

To change the default settings for future sessions of Minitab, choose Tools > Options > Control Charts and Quality Tools > Tests.

1 point > K standard deviations from center line
Test 1 identifies subgroups that are unusual compared to other subgroups. Test 1 is universally recognized as necessary for detecting out-of-control situations. If small shifts in the process are of interest, you can use Test 2 to supplement Test 1 in order to create a control chart that has greater sensitivity.
Benneyan Test, successive points equal to 0
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 that are 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.
K points in a row on same side of center line
Test 2 identifies shifts in the proportion of defectives for the process. If small shifts in the process are of interest, you can use Test 2 to supplement Test 1 in order to create a control chart that has greater sensitivity.
K points in a row, all increasing or all decreasing
Test 3 detects trends. This test looks for a long series of consecutive points that consistently increase in value or decrease in value.
K points in a row, alternating up and down
Test 4 detects systematic variation. You want the pattern of variation in a process to be random, but a point that fails Test 4 might indicate that the pattern of variation is predictable.
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