Q & A: Which rule is violated?

Posted by Sten Westgard, MS

An interesting question came from one of our readers, about how to interpret certain outliers.

So let's take one example, just two control values, expressed in z-scores. If the low control is -3.1  and the high control is + 2.3, which rule is violated? the 1:3s rule? The R:4s rule? Both?

An answer, after the jump...

First, let us assume that both rules are needed to properly control this method. In this case, when both the 1:3s and the R:4s are violated, it's helpful to recall what type of error is indicated by the violation of either rule. Both the 1:3s and R:4s are usually interpreted to point at a random error.

So in this case, we might dodge the question and say it doesn't matter which rule is violated, since they both point toward a random error source.

But if we complicated our situation. Say we have a method where there are eight values, consecutively  +0.2, +0.4, +0.7, +0.3, +0.6, +0.2, +0.4, +3.1. Now what rule is being violated? Is it an 8:x or a 1:3s?

These rules are different, of course. An 8:x rule points toward a drift or systematic error, while a 1:3s points toward a random error. However, since the 1:3s rule is in the same direction as the drift, we might take that +3.1s as simply another indicator of the drift, and the 8:x rule violation will take precedence.

It may be useful to think of those longer trend rules as taking precedence over the random error rules, particularly when those random errors are in the same direction as the drift.

However, this This can get even more complicated if random error truly "blows up", because then many different rules can be violated. Overall, though, we're usually trying to detect drifts, so if you see a 4:1s, or 8:x or similar rule is violated, that's probably the bigger error to investigate.

 Note: method performance has a role to play here.  If the method was a Six Sigma method, we would "turn off" most of the trend rules since a small violation on one side of the mean wouldn't be significant enough to impact the quality of the result. In those situations, your first violation might be just a 3s rule, and then during trouble-shooting and investigation, you might then pick up on the trend rules.

( Sorry, is this too complicated?  )