Run rules on 30,000-foot-level control charts

First of all, a 30,000-foot-level control chart is what Smarter Solutions teaches for baselining a DMAIC project metric and for use in scorecards at a business level.  While I will not go deep into the why we use this concept instead of the more common Shewhart SPC methods, I will cover it a bit.

Since most DMAIC project metrics are at a business level and they contain influences from different workers, different raw material batches, different types of transactions or products, …. the metric data stream is never a nice random distribution from a single process.  Most project metrics are truly a mixture distribution with a lot of items in the mix.  For this reason the Shewhart SPC chart selection rules do not apply very well and they will produce a lot of false indications of change.  This is the reasoning behind the IEE 30,000-foot-level methods.  To make it easier to type, I will call it the IEE method for the remainder of this post.

The IEE method uses only an individuals control chart for reporting the stability or predictability of a process.  Instead of selecting a chart to use, the lean six sigma practitioner needs to adjust or transform the data so that the Individuals chart will properly apply the control limits to recognize a special cause.  Once the data is control charted, the next question is to determine if it is stable or not.

When using the IEE method, it is understood that the data is not a pure random distribution.  If the data does appear to be normally distributed, it is because the process is managed that way.  There is no true expectation that the data is a true normal distribution, only that it sort of looks like one.  You do understand that a normal probability plot with a p-value > 0.05 only means that the data could have come from a normal distribution.  It does not say that the population is normally distributed.

Since we recognize that the data is normally shaped, but not truly normally distributed, then we should not apply any of the “Run Rules” to the control chart.  The run rules are created to indicate a special cause if there are patterns in the data that are not common in a true normal distribution.  Since we recognize that the distribution is not truly normal, we do not recommend using any of the run rules except rule 1: 1 point outside of the control limits.  There have been a few cases where we have also used the 9-points on the same side of the mean as an additional rule if process shifts are a potential result of a special cause event, but this rule is not used in general practice.

All of the other run rules are really comparing the probabilities of data occurring in specific standard deviation zones in a true normal distribution, which will cause a large number of false change indications if the data is actually a mixture that looks like a normal distribution.

I hope this makes sense.  No run rules on 30,000-foot-level charts.