A problem that has often confronted practitioners using control charts is when to consider recomputing the control limits. I’ve asked this question to several experts and researched it in numerous SPC texts. Oddly, either the issue is ignored or there is no clear answer to this important question. So I’ll offer my recommendation in this article.
Once control limits are established, they should not be changed without a complete investigation of the cause(s) and implication(s)*. Therefore, I propose the following action plan: The practitioner should evaluate the need to recalculate the control limits every time a statistically significant sign of instability is detected. A decision matrix for what to do is given in Table 1.
|Table 1: Decision Matrix for Control Chart Signals|
|Search for Cause(s)||Corrective Action(s)||Recalculate Limits|
|1. Cause(s) not found||None, continue search||No|
|2. Cause(s) found (the|
process has improved)
2. Can’t adopt
2. No (causes SPC problems)
|3. Cause(s) found (the|
process has degraded)
2. Can’t remove
Let’s discuss each case.
If the cause(s) are not found, then we should continue to search if it makes economic sense to do so [Tukey, 1946] and don’t recalculate the limits.
If the cause(s) are found and the process has improved, then we want to lock-in the improvement if possible. If it is possible to lock-in the process improvement, then the limits should be recalculated using data from the improved process otherwise they should not be recomputed. If it is not possible to lock-in the improvement, then serious SPC problems may ensue. For example, suppose that one production unit is upgraded and now performs significantly different than another but the low performing unit can not be upgraded, then mixing the data from these two units on a single chart will give rise to improper limits. In this case two charts are now required.
If the cause(s) are found and the process has degraded, then we want to take corrective action. If it is possible to fix the problem, then we should do so and not recalculate limits because the process should now have been returned to its previous controlled state. If it is not possible to fix the problem and a permanent change has occurred, then the limits should be recomputed with data taken after the change.
* Note: Some SPC software programs recompute the limits as each new point is added. This type of program can be used in the preliminary phase when we are trying to develop limits, but should NOT be used once the limits are established.
Tukey, J. W. (1946). Review of Deming, W. E., Statistical Adjustment of Data, Review of Scientific Instruments, 17, pp. 152-153.