1. Limits from Pre- or Post-Intervention
Farrokh Alemi, Ph.D.
These slides were organized by Dr. Alemi.

2. Pre-Intervention Post-Intervention
In these slides we point out that control limits can be calculated from pre or post intervention time periods. These results in different control limits and one has to choose the limits that are tighter, less spread from each other.

3. Separate Pre & Post Intervention Data
If there is an intervention, one must collect the limits from data prior or following the intervention. It is not reasonable to use all the data to calculate the control limits. Compare the chart in left to the chart in right.  Both are based on the same data, but in right the limits are based on the first 7 days, before the intervention.  The chart on the right shows that post intervention data are lower than LCL and therefore a significant change has occurred.  More points are lower than LCL in the chart to the right than the chart to the left.  By setting the limits to pre-intervention patterns, we were able to detect more accurately the improvements since the intervention.

4. Step 1: Check Assumptions
Control charts are based on comparing observations for each time period to control limits. If you make a change, you can see if the change has affected the outcomes.  This creates two time periods. The first pre-intervention and the other post intervention. One can set the limits based on the pre-intervention data.  Then you can compare post-intervention observations to project pre-intervention limits.  If any points fall outside the limits, you may then conclude that the intervention has changed the outcomes. The solid line shows the time period used to set the limit, the dashed line is an extrapolation of the limit to other time periods.

5. Select Control Limits that Are Tighter
Control limits can be calculated from per-intervention period and extended to the post-intervention period.  Or the reverse: control limits can be calculated from the post-intervention period and extended to the pre-intervention period.  Either way, we are comparing the two periods against each other.  But since the results will radically differ, it is important to judiciously select the time periods from which the control limits are calculated.  The selection depends on the inherent variability in the pre- or post-intervention periods.  Control limits are calculated from the time period with least variability. Typically, this is done by visually looking at the variability in the data or at the range of the data in pre- and post-intervention time periods.   

6. Select Control Limits that Are Tighter
This chart shows the control limits derived from pre-intervention data.  The control limits are calculated from the pre-intervention period and shown as solid red line.  They are extended to the post-intervention period, shown as dashed red line.  This control chart compares the observations in the post intervention period to the control limits derived from the pre-intervention period.

7. Select Control Limits that Are Tighter
This chart shows the control limits for the same data drawn from a post-intervention data.   Note that this time around the control limits are calculated from the post intervention period, shown as solid red line.  They are extended to the pre-intervention period, shown as dashed red line.  This control chart compares the pre-intervention observations to the control limits calculated from the post-intervention data.

8. Select Control Limits that Are Tighter
Note that both analyses are based on the same data. Both analyses compare the pre- and post-intervention data by contrasting the observation in one period to control limits derived from the other period. In one case, the control limits are drawn from the pre-intervention period and in the other from the post-intervention period. Note the radical difference of the control limits derived from the two time periods. In this case, the post-intervention control limits are further apart than the pre-intervention control limits. Therefore we need to select the pre-intervention period to estimate the control limits. Another way of doing this is based on the concept of Fourth Spread, which we will define shortly. If control limits are based on the time period with the smallest Fourth Spread, they would be tighter and more likely to detect smaller changes in the underlying work process.

9. Select Control Limits that Have Less Spread