ISO method for control charts for treating between-subgroup variability

Question

I have a question about control limits in control charts when there is between-subgroup variability.

Have you heard of the following method for calculating control limits?

* Calculate the traditional stddev, s, from all data values (with ignoring subgroup information).
* Calculate sigma = s / sqrt(n) where n is sample size of each subgroup.
* Set the control limits by [m - 3 * sigma, 3 + 3 * sigma] where m is the overall mean.

This method is explained verbally in "13.1 General caution" (pp.21-22) in ISO7870-2:2013(E).
A user in Japan requests this "ISO" method, but I myself had never heard of it.
(I myself think that JMP's three-way control chart is more understandable than this "ISO" method.)

yusuke_ono · Answer

Thank you all very much for your answers.

From your answers, I may now come to understand the strangeness of this ISO's recommendation.
 
If the assumed model is X{ij} = \mu + a_i + e_{ij} (where a_i is between-subgroup variability), then Var(\bar{X}) = Var(a) + (Var(e)/n). But the expectation of the estimation for Var(\bar{X}) by ISO's method is (Var(a) + Var(e))/n. It's biased.

If the assumed model is X{ij} = \mu + e{ij} (i.e. there is no between-subgroup variability), then the variance calculated by the ISO's method is unbiased, but we now lose the reason why we set subgroups (,and the ISO's method is not robust for the case when some \mu's are jumped or shifted).

Mark_Bailey · Answer

Adding to thoughts by Di and Dan, how do they know that the between sub-group variance was under control when they established the control limits? How did they verify that there were no special cause effects contributing to the between sub-group variance during data collection for determining the limits?

This practice might be set forth in an international standard but it is withouit merit or statistical rigor in my opinion. This situation is the motivation for the three-way control chart practice. Nothing is hidden and all levels of variation are monitored.

Dan_Obermiller · Answer

The purpose of rational subgrouping is to minimize the variation within a subgroup and monitor the variation between subgroups. By calculating the standard deviation, they are ignoring the two sources of variability. Why even subgroup the data? Why plot the mean?

As my colleague Di Michelson said:

"If there is different within and between variability, you should acknowledge that and use the appropriate variance component on the control chart. It’s easy to use the “right” formula for the variability of the plotting statistic, no need to get fancy with “wrong” formulas."

If they want to ignore the different variability sources, it seems to me that a Levey-Jennings chart (which uses the standard deviation) on individual data points would be more appropriate. Just not sure what this approach is trying to accomplish.