Revising Control Limits to Reflect Process Shift

03/17/2011:

I constructed a p chart of the percent of unacceptable pre-natal screening requisitions:

There were two major process changes (August 2009 and September 2010) during this time period. When do I add new control regions to the chart to reflect these changes? Do I wait until there are 20 points to the new process, or can I define a new region right away since I know the process is different?

Grace B., Quality Coordinator

Generally, new statistical regions are only applied to the chart when you have statistical evidence of a process shift. The p chart in the above figure shows no change to the process behavior (as evidenced by out of control or run test violations), in spite of the procedural changes to the process. This suggests the procedural changes had no significant impact on the process dynamics. The variation observed in percent unacceptable requisitions is the expected variation from a stable process.

When a special cause has been detected by the control chart (as an out of control or run test violation), resulting in a sustained process shift, then there is evidence of the process shift and it is appropriate to define a new control region for the process.

Nonetheless, it is possible the control limits in the above figure are biased by the inclusion of several distinct regions, which makes the chart somewhat insensitive to the differences between the regions. This sometimes happens in a retrospective analysis of a process; it is usually best to use control charts in real-time to detect these shifts as they occur. To simulate that manually, a control chart was constructed for the base period from January to July 2009 (assuming the process dynamics were relatively stable in that period), resulting in a center line of 5.6698, as shown in this new figure:

The remaining groups are then added back to the chart, whose control limits are preset based solely on the data from January to July 2009, as shown in a revised figure:

Since the control limits are defined based on the centerline from the initial region, they effectively investigate whether this subsequent data shows any evidence of a process shift relative to the initial baseline process. In this case, there is no evidence of a process improvement relative to the initial base period associated with the procedural change in August 2009; however, there is an out of control group detected in November 2010, which could conceivably have been associated with a change in September 2010. This would appear especially likely given the 3 groups in a row above the centerline (just beyond two sigma even!) beginning in September 2010. On that basis, it is reasonable to assert that the process had shifted in September 2010, but was stable from January 2009 until August 2010.

On the basis of the process shift in September 2010, a final p chart can be constructed as shown in this final figure with a new region beginning September 2010:

Note that, since there was no evidence of a shift until September 2010, the complete data from January 2009 until August 2010 is now used to calculate the control limits for the initial region (rather than just the initial base period used in the third figure above). The process would appear to be in control since September 2010. While it is curious that the initial 3 groups for the new region are above the centerline while the last 3 are below the centerline, there is insufficient statistical evidence at this time to draw any conclusions from the pattern.

Learn more about the SPC principles and tools for process improvement in Statistical Process Control Demystified (2011, McGraw-Hill) by Paul Keller, in his online SPC Concepts short course (only $39), or his online SPC certification course ($350) or online Green Belt certification course ($499).