The Importance of a Proper SPC Subgroup Sampling Technique

Methodically finding useful data in out-of-control conditions

A common error of many Six Sigma and operations research professionals is not properly selecting the correct subgroup sampling technique when constructing a statistical process control (SPC) chart. Incorrect subgroup sampling technique selection has become worse in the modern computing age, perhaps because most practitioners try to “fit” their data into the graphical user interface template of the major statistical software packages. Consequently, many practitioners produce aesthetically appealing charts that are simply not effective at identifying out-of-control (OOC) conditions. This article will discuss proper SPC subgroup sampling techniques and illustrate the principles of proper subgroup sampling selection from a practitioner’s perspective.

The proper selection of an SPC sampling technique should be based on an analysis of historical data that is representative of the current process and the question that needs to be addressed. The importance of selecting the proper SPC subgroup sampling technique cannot be stressed enough—however, it is overlooked by most practitioners.

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Imaginary Processes

It is meaningless to discuss rational subgrouping in an imaginary theoretical normal process.

You would be well advised to read Wheeler's book "Advanced Topics in SPC".

Sampling from a Trimodal Distribution

I guess I missed something. I see a "trimodal" distribution. And the X-Bar/R Charts appear very similar in shape. At least it appears that no matter what sampling plan was selected, both ended up with similar results. I think only one point different(?)

It appears to me that the sidemodes are from the early groups and last sample groups. Given these data, I didn't see much of a difference in the charts or analysis presented -- enough to draw a conclusion that subsampling change had any impact at all.

Dan

100% data

I still have some doubt as to how to chart 100% data. It seems like the only way to chart 100% data is with an I-MR chart. Any kind of X-bar - MR chart will violate rational sampling. Or is a better solution to periodically draw X-bar subgroups form the 100% data, in order to get a better sense of mean shifts? It just seems counter intuitive to only use part of the data if 100% data exists.

By the way, I agree with referring to Wheeler.

A couple of points...

First, I don't think you missed anything, Dan. The little piles of data above and below the center pile are from the data in the high and low "out-of-control" points on the Xbar-R charts.
Secondly, I'm glad we have an article that talks about rational subgrouping; this is an important subject that deserves a lot of discussion, especially these days when there are too many Black Belts and Master Black Belts who have too little understanding of SPC. However, these examples may not be the best to illustrate the concept.
For one thing, sampling theory as usually practiced for enumerative studies may be completely irrelevant in analytic studies; monitoring process data over time for SPC usually falls under the latter type. There is no underlying population. There may be a pile of historical data, but our task is not extrapolating from a smaller samples to characterize the population, it is to extrapolate from the past to the future. The population of interest does not exist, and never will.
The control chart indicates that we do not have "normally distributed data." You never actually have normally distibuted data, but when you have an out-of-control condition, you can't say anything at all about the distribution; without homogeneity, there is no distribution. In fact, what we appear to have in this case is maybe three different distributions. Further study within the lots to find out whether they are interenally homogeneous might be helpful, as one of the primary goals of rational subgrouping is ensuring internal homogeneity.
You could, I think, make an argument that either scheme discussed here might work. While it's true that the chart for "last five" reveals one extra assignable cause signal, the chart for the "random sample" has a smaller R-bar, thus tighter limits; it may, therefore, be more sensitive and stand a better chance of revealing other signals over the long run.
Anyone interested in really exploring rational subgrouping would do well to study closely chapter 5 (especially sections 5.6-5.7) in the Wheeler text John cites.