Control chart for individual measurement (g-chart)

The G chart (or Geometric chart) is used when the incident of interest is relatively rare and some some discrete determinaton of opportunity (cases, patients, admits, line insertions, and so on) can be obtained. The G chart allows each occurrence to be immediately evaluated on the chart rather than having to wait to the end of a time period before the data point is plotted. The G chart is particularly useful for verifying improvements (such as reduced infections) and for processes with low rates.

Improvements are indicated by higher values (more cases between incidents) on the G chart. Because of the skewed nature of the geometric distribution, there is no lower control limit for the G chart, but the standard run rules can be applied because the center line is adjusted to the theoretical median of the distribution.

The calculations of control limits is based on the geometric distribution:
Determine the incident of interest (for example, pressure ulcer) and the unit that determines the opportunity for the incident (for example, occupied bed days).
`g` = number of opportunities or units between incidents
`bar g` = average of g
CL = LN(2)`times bar g`
UL = `bar g + 3 times sqrt(bar g times (bar g + 1)) `
LL = there is no lower control limit

Notes:

• The UL is approximately 4 times g_bar (or 5.7 times the CL) for quick visual analysis.
• Since the count data on a g chart are usually highly skewed, the plotted data will not be symmetric around the average (g_bar). The theoretical median = LN(2) * mean for the geometric distribution should be used for the center line when it is desirable to apply the shift rule (8 consecutive points above or below center line).