The calculation of control limits is based on the geometric distribution. Event probability and alpha are used to compute the non-symmetrical limits. An "out-of-control" signal above the UCL is desirable, indicating a significant increase in units/opportunities or days between adverse rare events. See Benneyan, 2001.

SigmaXL adjusts the Benneyan CL and LCL by subtracting 1 as done in the UCL and does not round the limit values. Opportunities between events are counted as 0, 1, 2, 3, … (a=0 in Benneyan Table 3).

- Click
**SigmaXL > Templates & Calculators > Control Chart Templates > Rare Events > Rare Events Prob G**. This template is also located at**SigmaXL > Control Charts > Control Chart Templates > Rare Events > Rare Events Prob G**. - Open
**Doses Dispensed Between Adverse Drug Events.xlsx**(**Sheet 1**tab). Adverse Drug Events (ADE) are rare, so Doses Dispensed Between ADEs is used as a health care metric. The data is discrete and distributed geometrically, so the G chart is appropriate to use here. The event dates 7/2/2019 to 9/24/2019 are “Before Improvement” and the Doses Between ADEs will be used to calculate the control limits. Dates 9/28/2019 to 1/17/2020 are “After Improvement” and the Doses Between ADEs will be added to the control chart. The goal is to decrease the occurrence of ADEs which will increase the doses between, with an “out-of-control” signal above the UCL being desirable and confirmation of the improvement effort. - Copy the “Before Improvement” data in cells
**A1:B21**and Paste Values to the template at**A1**. This will overwrite the formulas in Column B. Adjust the template column widths as necessary. - We will use the default
**Alpha UCL**= 0.00135 (this corresponds to the one-sided probability for UCL in a classical Shewhart control chart with 3 sigma limits). Click the**Rare Events Prob G Chart**button to create the Rare Events Probability Based G Control Chart: - This confirms that the process is “in-control”. Note that the probability based UCL is much larger than the one calculated above for the regular G chart.
**Tip**: If the UCL is considered to be “too large” for practical use, adjust the**Alpha UCL**to a larger value, for example, .01 instead of .00135 and recreate the control chart. Note however that this will increase the Type I (false alarm) rate.- Although the process is “in-control”, as a critical health
care metric, efforts were made to improve the process and this
data will be now added to the chart. Switch back to
**Doses Dispensed Between Adverse Drug Events.xlsx**(**Sheet 1**tab). Select and copy the “After Improvement” date/times in cells**A22: B31**as shown. - Switch to the Rare Events Prob G Chart template and Paste
Values to cell
**A22**as shown. This will overwrite the formulas in Column B. Adjust the template column widths as necessary. - Click the
**Add Data**button to add the new**Doses Between Events**data to the Rare Events Probability Based G Control Chart: - This confirms that the process is now “out-of-control”, so
the improvement efforts to decrease the occurrence of ADEs and
increase the Doses Between have been successful. Note that the
control limits should be recalculated with just the “After
Improvement” data when 20 data points are available.

1. This Rare Events Prob (Probability-Based) G Control Chart
template should be used with days or units/opportunities between
(typically adverse) rare events.

2. You can replace the **Date/Time** and **Days
Between** column headings with any headings that you wish.

3. Enter date in the **Date** column. Days between are
automatically calculated and entered into **Days Between**
column. Cell B2 is not used in this case.

4. Alternatively, you may manually enter data in **Days/Units
Between**. Note, this will overwrite the cell formulas.

5. Enter **Alpha UCL**, typically 0.00135,
corresponding to the one-sided probability for UCL in a classical
Shewhart control chart with 3 sigma limits. This will also be
applied to the LCL if greater than 0.

6. The calculation of control limits is based on the geometric
distribution. Event probability and alpha are used to compute the
non-symmetrical limits. Calculated event probability is noted on the
control chart.

7. Optionally enter the historical **Event Probability**.

8. Click the **Rare Events Prob G Chart** button to
create a control chart. This will overwrite any existing control
chart.

9. After the control chart has been created and additional new
**Date** or **Days/Units Between** data
entered, click the **Add Data** button to add the data
to the existing chart. Control limits will be calculated using the
original chart event probability or specified event probability.

10. Add Data should only be used if there are at least 20
observations in the original chart or known historical Event
Probability has been specified.

11. An "out-of-control" signal above the UCL is desirable,
indicating a significant increase in days or units/opportunities
between adverse rare events.

12. Reference: Benneyan, J.C. (2001), "Performance of Number-Between
g-Type Statistical Control Charts for Monitoring Adverse Events",
*Health Care Management Science*, 4, pp. 319–336, Table 3.

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