X-MR Control Chart Rules (Particularly the MR)

Matt's Quality Handle

Involved In Discussions
#1
Please bear with me, it's been a while since I actually statisticed.

I'm setting up X-MR charts for a chemical process (extracting a protein from a biological source), whereby certain characteristics are sampled from a finished batch. The business goal is to automatically plot based on the results of our finished goods. We have a data visualization tool that publishes the charts, and can send email alerts for certain conditions (i.e. a rule is violated). So I'm using Excel to put formulas in to perform the control chart tests, which then gets vacuumed into our data visualization tool.

In searching for web literature, I found these posts, which independently (or maybe dependently, although sources aren't cited) call for the same tests on MR charts.

Using tests for special causes in control charts - Minitab
Applying the Out of Control Tests | BPI Consulting (spcforexcel.com)

Since MR is by definition the absolute value of the change, what does 6 (or 7) points increasing/decreasing indicate is actually happening with the process? Same with the 14 points alternating up and down. As I wrestle with it mentally, I'm struggling with how this test is relevant when directional indication (the +/- sign) is removed.
 
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Steve Prevette

Deming Disciple
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Super Moderator
#2
What is happening in X - mR (including Xbar -R) is we really have two different measures going on. We have - is the central tendency stable (the traditional X chart). But my average can remain constant, but my variability may be significantly increasing, and that would be picked up first by the mR chart. Of course, if the variability increased ENOUGH it will eventually be detected on the X, I, Xbar charts, but it can remain hidden for some time.

So we should use the same rules on the mR (or even Sigma) charts for detecting a trend as we would on the individuals or xBar chart.

Also, some will point out that unless my moving Range or average Range chart is stable, I really don't have a good standard deviation I can apply to the individuals chart.
 

Bev D

Heretical Statistician
Leader
Super Moderator
#3
I'm setting up X-MR charts for a chemical process…

Since MR is by definition the absolute value of the change, what does 6 (or 7) points increasing/decreasing indicate is actually happening with the process? Same with the 14 points alternating up and down. As I wrestle with it mentally, I'm struggling with how this test is relevant when directional indication (the +/- sign) is removed.
First remember that the SD also is ‘directionless’. The Moving Range is similar to the SD in that a small MR means that the two averages are close to each other and a large MR means the two averages are far apart. So if the MR chart shows that 6 or 7 points in a row are increasing it means that each successive average is moving further away from the subsequent average than the last pair. (Draw it out - it helps to visualize it). Alternating large and small MRs indicate that you have a pair of averages that are far apart, the next average is close to the second average, then the 4th average is far away from the 3rd average, etc. (again draw out the description…). This can be an indication of ‘over control’. I suggest thinking about how your process can produce these results. (In my experience with I, MR charts for processes such as you describe the average chart is better at detecting changes and interpreting what is happening. To the extent that I often would suppress the visualization of the MR chart and only display the average chart and the within subgroup chart…)

To add to Steve’s point regarding a ‘good‘ SD, most processes are not stable when we first chart them. But they do provide us with the information to begin diagnosing them…although many people are surprised that often processes they think are unstable actually are when properly plotted. It’s just that the variability is too large for their liking…
 

Welshwizard

Involved In Discussions
#4
Hi, looking at your original question it would seem that you require clarity on what rules to use for the moving Range Chart which accompanies the Individual or X Chart.

The traditional tests you reference via your Minitab link do not apply to the moving Range Chart except for the the point outside the 3 Sigma limit. The reason they don't apply is due to how the moving Ranges are computed and their correlation to the individual points themselves.

If you use the traditional tests with the moving range chart you will tend to create false alarms and since the reason you are using a chart in the first place is to act on the signals you would end up wasting your time chasing your tail to no advantage.

Actually, in order to detect shifts in the routine variation would require much more data than the traditional tests.

A lot of this confusion is due to software packages that automatically by default apply the traditional tests to both charts, in some cases you cannot even turn them off.

For validation of what I have said and more useful information on ImR Charts please look at www.spcpress.com/pdf/DJW250.pdf. Dr Wheeler explains it beautifully.

Hope this helps
 
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