On non-homogeneity and predictability: when statistics and SPC are taught and for many of the inferential statistical tests, the ideal state is a homogeneous random population. (think about the math for a minute: a homogeneous random population - which is redundant - is one where the average (location) and the standard deviation (spread) are primarily caused by the same factor(s). so the mathematical tests that predict the variation of the average form the standard deviation works. and when an "assignable cause" occurs to move the average (location) but not the standard deviation, the formulas will 'detect' that he variation in averages is not within the expected range (standard error of the mean). However, and this is a huge however, many processes are simply not homogenous. There are two basic types one might think of:

- multiple process streams are combined and there is a systemic difference between the streams (such as with cavities in a mold or across a web of material etc.)
- where there are multiple natural components of variation such as lot to lot or within piece in addition to the 'ideal' piece to piece variation.

Rational subgrouping was developed to handle this. I have many examples of this - see my resource on 'profound statistical concepts' for two such examples. sometimes these processes are unstable and some times they are stable; sometimes they are capable and sometimes they are not...

(by the way my comment regarding plugging numbers into statistical software was not aimed at you - it was a general reminder to the many poor souls who are given a job where statistics is required but they get no critical training...)

some articles from Donald Wheeler:

Wheeler, Donald, “

*What is a Rational Subgroup?*”,

*Quality Digest*, October 1997

SPCTool
Wheeler, Donald, “

*Good Limits from Bad Data Part III*”,

*Quality Digest*, May 1997

SPCTool
Wheeler, Donald, “

*Can I Have Sloping Limits?*”, Quality Magazine, May 1999

Wheeler, Donald,

*“The Three-Way Chart”*, Quality Digest, March 2017

The Three-Way Chart | Quality Digest
Thanks for taking the time to reply.

On your examples of non homogeneity;

- The two examples you have given are of course not rational in the sense that you wouldn't expect them to demonstrate homogeneity for the reasons you have outlined, due to this it would be futile to plot this data on a process behaviour chart.

Even if the notion of homogeneity is satisfied in our minds for the organisation of the data it doesn't mean that the process will display predictability "straight out of the box". We will usually have to work on this by chasing down the causes of exceptional variation and in this way constantly improve the process.

I think we differ on the definitions for homogeneity, I find it easier to explain without the possibility of confusing people with standard deviations and process averages thus:

Stability and Predictability are descriptions of the

**underlying process.**
Homogeneity is the property of the

**data** produced by a predictable process

Thinking about variation and how it works;

The factors we control do not create the variation in the product stream. We choose the levels for the control factors to obtain the desired process average.

The uncontrolled factors create virtually all the variation in the product stream but there will be a pareto effect among these uncontrolled factors. There will be a few dominant factors and a large number of trivial factors.

The uncontrolled factors can be classified in two groups according to the type of variation present.....dominant cause and effect relationships will be assignable causes, these will move the process around to create exceptional variation. The large number of trivial uncontrolled factors will be the common causes of routine variation.

Thanks for your references of Don, I have had the privilige of studying with him for the last 15 years or so I am very aware of all these references. A few years ago i asked similar questions about homogeneity as I asked you and this reply contains much of this thinking.

The confusion from me surrounded your initial statement below

"While control charts are designed to detect nonhomogeneity, a nonhomogenous process can be quite stable and predictable. Rational Subgrouping was developed to handle stable nonhomogeneity"

A non homogenous process can be worked upon to be made homogenous and thus stable and predictable but only if the data is rationally subgrouped in the first instance i.e. the data is arranged in a rational common sense way.

Cheers