Control Chart Templates: Rare Events Prob G Chart

Rare Events Prob G Chart - Introduction

The Rare Events Prob (Probability-Based) G chart (or Geometric chart) is an alternative to a standard attribute chart when the adverse event of interest is rare and discrete opportunities between events are counted (e.g., number of units or days between). The use of probability-based control limits is recommended in order to properly control the Type I (false alarm) error rate.

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.

PROBGTESTINTRO

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.

Template Notes and References:

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.