EasySPC P Charts and Ratio Guidance

P Charts and Ratio Guidance

Some customers need data similar to the following table presented as an SPC chart:

A P chart looks like the right choice. However, the numerator is at times larger than the denominator, resulting in percent greater than one.

So how do we best plot and choose a chart?

Attribute charts (P, U or C) would not be appropriate to use in this instance for the following reasons:

• The Actual events data is already calculated as the observed rate/ 1000 case by AHRQ1
• The Expected events is estimated from a model based on a reference sample and converted to an estimated rate/ 1000 cases
• The Expected events is not the denominator as would be normally used in the calculation of limits for P and U charts as it is neither the total population of cases nor is each expected event data point is not independent of each other.

This means that whilst the observed to expected is a ratio it is not a rate or proportion. Such data cannot meaningfully be placed on a P chart. They must be charted using a XMR chart.

The figure below is provided by Donald Wheeler to describe this approach:

Options to consider:

1. Plot the O/E Ratio as an XmR Chart rather than P-chart

This is the most appropriate chart to use as outlined in Understanding Statistical Process Control

2. Plot the Observed events and Expected events as separate XmR charts and compare

Whilst this is useful, it does not provide the requirements of the client and adds no additional information by creating an additional chart

3. Plot the Actual Events as an XMR chart and overlay the expected events

This is as advised by the Health Care Data Guide (p.368, Provost C Murray, 2022).

The chart may be difficult to interpret, if users are unaware which of the data was used to calculate the control limits.

This type of chart is not currently available out of the box in EasySPC, however is on the roadmap as a potential future development. However, there is a ‘workaround’ which may suit you (screenshot example above). Note this isn’t the same data as previous examples in the document.

To do this you can use the target line (or ‘Specification limits within ‘Capability Analysis’) as a measure and plot the ‘expected’ using this.

4. Plot the difference between observed and expected events as an XMR chart

Bibliography

• Hart, M.K., Robertson, J.W., Hart, R.F., C Lee, K.Y. (2004). Application of Variables Control Charts to Risk-adjusted Time-ordered Healthcare Data. Ǫuality Management in Healthcare, 13(2)
  https://journals.lww.com/qmhcjournal/fulltext/2004/04000/application_of_variabl es_control_charts_to.3.aspx
• Provost, L.P., C Murray, S.K. (2022). The Health Care Data Guide Learning from Data for Improvement (2nd ed.). John Wiley C Sons, Incorporated.
• Wheeler, D.J., C Chambers, D.S. (1992). Understanding Statistical Process Control (2nd ed,). SPC Press.