I-MR Chart vs. X-bar & R Chart - Differences

Hi all,

I would appreciate your help in simply explaining to me the differences between an I-MR Chart and an X-bar & R Chart. What are the differences, why would you use one vs. the other, what are the benefits and drawbacks, how would we move from an X-bar & R chart to an I-MR chart, etc.

I am moderately familiar with X-bar & R charts, but have no experience with I-MR charts. I have checked previous threads, but couldn't find one that was more explanatory in nature.

Any help would be appreciated!!

Thank you!

Izoyd said:

Hi all,

I would appreciate your help in simply explaining to me the differences between an I-MR Chart and an X-bar & R Chart. What are the differences, why would you use one vs. the other, what are the benefits and drawbacks, how would we move from an X-bar & R chart to an I-MR chart, etc.

I am moderately familiar with X-bar & R charts, but have no experience with I-MR charts. I have checked previous threads, but couldn't find one that was more explanatory in nature.

Any help would be appreciated!!

Thank you!

Click to expand...

The NIST/Sematech eHandbook of Engineering Statistics is an excellent source for answers to this type of question.

The key difference is if you have little within-sample variation (you typical 5 piece sample, for example), then the range will not represent the long term variation of the process. So, I -MR uses longer time sequence to detect change, assume that 5 samples over time will better represent the long term variation. One thing about traditional SPC, if your sample does not represent the long term variation, then it is not going to mean much when you try to look for trends and shifts.

The I-MR chart is used when there is no reason to do subgroups (R Chart), one must not subgroup the data unless there is a reason (relationship between such sets of data, not because you need to do so because the R-Chart you learned used 5 data points).

The I-MR is used in continuos processes (ie. chemical industry).

Thank you gentlemen for the input. I have done some additional research and I think I understand things now. A good website I found was: http://www.qualityamerica.com/knowledgecente/knowctrINDIVIDUALX_MOVING_RANGE_CHARTS.htm

However, I have a further question now. From what I can tell there are two ways to calculate control limits for the I-MR charts.

For X-UCL and X-LCL you can either use:
1) X-bar +/- (3 SD) OR you can use
2) X-bar +/- E2MR-bar.

I was told using #1 is considering X & R to be separate sets of data, whereas #2 shows more of a relationship between X & R, but that this is more a principle of theory.

What I'm confused about now is when you would use one set of equations over the other as the actual calculations do vary between the equations? Is it simply theory? Or is there some other consideration?

Again, I appreciate your help!! I think I'm almost there in understanding for your average quality engineer (and not a statistics expert)...

I found an article in Quality Digest that I think answered my question. I've attached it for anyone else who may wonder: "Individual Charts Done Right & Wrong."

That is the better source. Davis Balistracci also has a series of similar articles in recent issues of quality digest that are similarly helpful

The key to understanding if a control source is reliable is the level of statistical theory that it espouses. The more the theory the less reliable the source. Control charts are not statistically sophisticated. I strongly recommend that you read Donald Wheeler's work and Davis Balistracci's work to get begin understanding these charts

And in answer to your last question #2 is the correct formula. You should never use +|- 3SD as your limits.

Bob, sensible advice like this on using Imr charts is hard to find. Your statement about capturing the proper representation of the common cause variation is perfect. We collect a sample every 4 hrs. We have up to 16 cavities when we take a sample. so our reason is primarily time and metrology cost since we would have to take, say 5 shots to use XbarR. But the better argument is that we get a better representation of the process variation by Using Imr and sampling every 4 hrs.Thank you so much!

Your best approach is to do a process capability - by cavity - to find out which cavity shows the most variation - near the vent, near the runner, near heaters, near cooling runs, etc. Based on that, pick the cavity that has the most variation and plot it on an IMR. If you need more that one chart for more than one cavity to find the one that has the loudest "voice of the process", then that is a good idea for the short term.

Also, the capability should yield the best sampling frequency. Just as in machining, in molding there should be at least 5 sampling times between any adjustment or significant change - including possibly addition of material to the feed if it shows up as statistically significant. I am not sure 4 hours is sufficient sampling rate. That would mean you can run that process for 20 hours with no operator intervention.