How to create a range control chart based on the median range and not the average range

[#1]

Is there any easy way to use JMP 13 to create a range chart based on the MEDIAN range and not the average range? (Hence the upper range limit would also be based on the median range as well.)

If not I assume one option is to use the run chart and adapt it through scripts. I'd put the range values for all the subgroups into a list, find the median of this list, and then take it from there (i.e. adding reference lines through scripting with the central line the median range and the upper range limit the median range multiplied by the appropriate bias correction factor). 

Any comment / tip would be welcome. 

Scott.

[#2]

Hi @scottahindle, I can't find anything to suggest that is supported in JMP currently, but it would be relatively easy to incorporate by using the Control Limits column property for the individuals and moving range charts.  That would allow you to implement your custom limits within Control Chart Builder.

[#3]

Hi,

you need to use the Individual and Moving Range Chart option directly and not through the Control Chart Builder. To do so:

Menu Analyze -> Quality & Process -> Control Chart -> IR

There you can select Median Range instead of Moving Range

The results would e.g. look like this (left Median range, right Moving Range)

This is in JMP 13 and I guess previous versions available. The calculation of median range is documented in the Quality & Process User Guide PDF under Help-> Books -> Quality and Process Methods

The script would be similar to:

Control Chart(
	Group Size( 1 ),
	KSigma( 3 ),
	Chart Col( :CI, Individual Measurement, Median Moving Range )
);

where :CI is the process variable you want to analyze.

[#4]

The workarounds here have been great for earlier JMP versions. I am pleased to report that Individuals and Median Moving Range charts are supported in Control Chart Builder as of JMP 15. 

[#5]

Hello Audrey, Thanks for the comment and yes I have used the median moving range for some of charts for individual values in recent months. My question wasn't about individual values but rather subgrouped data where I would use e.g. an average and range chart (X-bar R chart). Unless I've missed something my "wish" still remains a "wish". In some cases I would prefer to use the median range and not the more standard average range. I put in this request in 2-3 years back Use of median range for average and range chart 

[#6]

Thanks, Scott, that helps. It's good to know this is still an active "wish" and wasn't fully addressed by the change i found which i thought was the same as your request. I asked around to get some more clarity on the issue. It has led to some discussion, including a search for this idea in existing research as a valid measure of dispersion. (We must have valid references to add new computations to JMP.)

To be clear: i think your request is to use Median Ranges as a measure of dispersion, rather than traditional Range values or Std Deviation values. So instead of XBar-and-R, or XBar-and-S as the paired location-and-dispersion chart, you're looking for an XBar-and-Median-Range pair of charts. Does that sound right to you?

We finally did find a reference to Median Ranges used in the dispersion chart here: https://www.spcpress.com/pdf/DJW207.pdf. We are entering a fresh request for this, based on this reference, and now that we understand your request better. It is not something we have commonly seen and is not currently done in JMP or SAS, but there is a precedent for it. Please feel free to take a look at the paper and add additional comments and clarifications here if you wish.

In the meantime, I asked for an example within JMP already that might be closer to what you're looking for and was given the idea for Individual on Means chart which does use the median. Note the name of the chart uses "Individual" but you can use it with subgroups as well. Here is an example using sample data. 

dt = Open( "$SAMPLE_DATA/Big class.jmp" );
Control Chart Builder(
    Variables( Subgroup( :age ), Y( :height ) ),
    Chart( Position( 1 ), Limits( Sigma( "Median Moving Range" ) ) )
);

[#7]

Scott, could you provide an example of when you would use the median range?  I would be really interested in a real life application and how the median rage improved on analysis using control chart method.

Don (in the referenced paper) states:

"In general, for the default computation, the Average of your Within-Subgroup Measures of Dispersion is recommended. However, in those cases where some extremely large values may have inflated this average, you may switch to using the Median of your Within- Subgroup Measures of Dispersion to improve the sensitivity of your analysis." I would think using the median range would give you smaller values when there are extremely large ranges, which would result in tighter control limits (I suppose what Don means by increased sensitivity).

But, isn't the idea of the control chart to:

1. Determine if the within subgroup variation is consistent and, if the within subgroup variation is consistent,

2. Compare the within sources to the between sources to determine which has greater leverage

If you have extremely large ranges wouldn't you want to know why?  I'm not sure how using the median would provide improved insight to the questions the control charts answer.  Just because you can calculate a median range doesn't make it useful.

[#8]

Agree that the default computation of the average range provides the insight to examine the predictability (or lack of it) of the process.  As you state, however, large range values will inflate the average range, thereby widening the limits on both the range chart as well as the average chart.  Without the need to delete any data, the median range is then more likely to give a better idea of the level of routine variation to expect IF the inconsistencies (causing the inflated ranges) are better controlled and their effect eliminated. (If we use a control chart surely our idea is to seek to take action on the special causes? The median range can give a better idea of what to expect if this action is successful.)

JMP makes it easy to eliminate points from calculations (by excluding rows) which one can do if persisting with the average range. But, a simpler way to approach this, where the average range is inflated, is to use the median range rather than keeping the average range and exercising judgement on which range values to keep/delete from the computations. 

The median range is simply something that on occasions can help to gain additional insight. It is a simple procedure - the use of the median range as Wheeler explains in the above cited paper - so why not have it available to help us in our work?

[#9]

The Wheeler paper is just meant to compile the multiple types of charts available. If you look at Table 1 (Which Chart to Use), those are the charts Wheeler recommends. I'm confused by your use of the charts. You indicate deleting data? Why? The most important information is being deleted? You should understand why those special causes happened and fix the process. Why is the range inflated?
What is meant by "routine variation"? You mean common cause variation? Again the charts perform 2 functions. The range charts (R or MR), and only the range charts, assess stability/consistency and provide insight to the nature of the variability (special/common cause using Deming's vernacular). The Xbar (actually most often the Ybar) is a comparison chart to provide a comparison between the within and between sources of variation.
Again, my question was: Can you provide a real life application example that benefits from using a median range vs. an average range? How is the median range providing "additional insight"?
You are right about one thing, JMP or any statistical software, makes it way too easy to manipulate the data.

[#10]

I think we are closer in thinking than your last response would suggest. You can read the papers I published on Quality Digest to see that I would not delete data without valid reason. Two of my many learnings from Dr. Wheeler's SPC seminar were (i) that outliers are the most important values in your data set, and (ii) the possible use of the median (albeit on rare occasions).

Thought experiment: You have ten subgroups and one of these subgroups has a big range. The helium source going into a device hadn't been changed when it should have been and measurements weren't working as usual, i.e. inconsistent. What to do? Take the learnings from the special cause e.g. update procedures so that the helium source is changed more timely, either by increasing the frequency of change or by more frequent monitoring of its properties to know when the helium change should be done.

If these ten subgroups were my baseline data I'd get inflated limits due to this one big range. The median range from all ten subgroup ranges, without the need to delete the "special cause" from the data set, would still give me a sound estimate of my routine (common cause) variation. The average range would be inflated.

As said, my realisation of the potential value of the median came from Dr. Wheeler's SPC seminar. How often would I use the median range? Not too often, but to have it there is useful. (From the software perspective I assume it would be pretty easy for JMP, or whichever software supplier, to introduce the median range as a complement to the average range.)

I will write up one of my examples in Quality Digest at some point.

Hope this helps.