G charts, like T charts, are used to plot rare events. The G chart uses the geometric distribution of the number of opportunities between events.
The data for this recipe uses the number of days between incidents at a factory. The worksheet lists this information as days until an incident has occurred. We will plot the number of days between accidents to look for unusually high or low numbers of days.
The following steps will create a G chart of the number of days between accidents at a factory:
- Open the
Accidents.mtwworksheet using Open Worksheet… from the File menu. - Navigate to Stat | Control Charts | Rare Event Charts and select the G… option.
- Change the drop down for Form of data to Number of opportunities and the Method of counting opportunities drop down to Opportunities between events.
- In the Variables: field, enter
Days. - Select G Chart Options… and navigate to the Tests tab.
- Select Perform all tests for special causes.
- Click on OK in each dialog box.
The G chart is named for the geometric distribution. This produces a chart that is similar to the T chart. T charts are typically used for time between events where a Weibull distribution would be fitted to the data. The G chart plots discrete intervals or the number of opportunities until an event. It would be more accurate to plot the total number of employee days between events but in most cases, it is simpler to list the number of actual days.
Other examples of when a G chart might be used could include the number of days at a hospital until an infection in a patient is observed. Again, while it would be more accurate to give out the total number of beds occupied until an infection, this would more typically be replaced by days.
Like the T chart, higher values on the chart indicate an increase in the number of opportunities until an event occurs. In the used data here for incidents at a factory, higher results are better.
The first test for special causes has an interesting problem with this chart. The lower control limit often sits at 0. Test 1 looks for data that falls outside the control limits to indicate a result that is unusually high or low. As negative days between events can never happen, we would not cross the lower control limit. This makes it difficult to find events that show unusually short days between events.
The Benneyan test is used for test 1 on the lower control limit. This looks for a number of consecutive plotted points that lie on the lower control limit. The number of points that will be highlighted as unusual is based on the mean of the data.