topic Re: How to create a range control chart based on the median range and not the average range in Discussions

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

scottahindle — Wed, 07 Feb 2018 21:50:37 GMT

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.

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

cwillden — Thu, 08 Feb 2018 19:44:35 GMT

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.

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

martindemel — Mon, 05 Mar 2018 12:00:31 GMT

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.

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

Audrey_Shull — Mon, 11 Jan 2021 21:06:26 GMT

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.

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

scottahindle — Mon, 11 Jan 2021 21:54:36 GMT

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

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

Audrey_Shull — Thu, 14 Jan 2021 20:54:19 GMT

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" ) ) )
);

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

statman — Tue, 12 Jan 2021 20:00:27 GMT

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.

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

scottahindle — Fri, 15 Jan 2021 07:52:02 GMT

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?

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

statman — Fri, 15 Jan 2021 15:21:49 GMT

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.

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

scottahindle — Mon, 18 Jan 2021 09:49:24 GMT

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.

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

statman — Mon, 18 Jan 2021 16:41:19 GMT

Scott, I love your thought experiment, so I will continue it.

First I will reiterate: Range charts answer the question: Is the variation within subgroup (which is a function of the X's changing within subgroup) consistent, stable (therefore predictable)? If not, you should examine the X's changing within subgroup for their possible effect on Y. The control chart, in this case the range chart, is meant to help identify those "unusually large sources of variation". Sometimes the special cause (Don likes to call it assignable cause) is obvious and you don't really need any statistical tests (control limits). Xbar charts are comparison charts. They compare the within sources of variation (represented by the control limits) to the between sources (represented by the plotted averages) to determine where is the leverage (where should understanding the process continue?, which set of X's should you further investigate?).

OK, let's say you have narrowed it down to something about helium source. Of course there is more than one variable changing within subgroup and one of them is something about the helium source (though you do not suggest what?). Is there insufficient amount? Is the concentration varying? Are there contaminants? You want the charts to identify these "events" so you can act appropriately on the process. The chart accomplished its purpose. My guess would be that this happens to the helium more than once...it really isn't special, just special based on the time series or sampling plan you chose. The action you take would look common cause like (change the process) to prevent this in the future (really not special). If you change the process as a result of what you learned, should you use the data from the "old" process?

I don't know what baseline data is, but I'll suggest you are using the 10 subgroups as a basis for comparison and decision making. Why 10? My guess is you think these 10 will provide a representative estimate of the variability in the process (of what some may call the common cause variability). 10 because you believe that in 10 you will see the influence of the X's you hypothesize will effect the Y's (they will change enough over the 10 subgroups...). But, contained in these 10 is an unusual "data point" that exhibited itself by creating a large within subgroup range. What caused this data point? Was it measurement error? Or due to then other X's changing within subgroup? Certainly you would be confident that it is something to do with the X's changing within subgroup (Assignable to the within subgroup X's) as there are NO between subgroup sources captured in the Range statistic. I'm a bit confused by your helium hypotheses, because if the helium is deteriorating over time it would likely show up on the Xbar chart, but I'll play along. Perhaps the variability from the helium effect was actually present in all of the data points and only exaggerated in the one data point causing the OOC condition? Or perhaps the helium was only part of the issue? Should you use the rest of the data to compare the within and between sources? Or should you develop a new sampling plan and get new data? Hmmm, the way I understand it is you start with hypotheses (and predictions made about the effect of the hypotheses), get data to provide insight to your hypotheses (and to determine how good were your predictions) and then understand what was learned, drop/add/modify your hypotheses and run through the cycle again. For your thought experiment: These X's captured within subgroup (change at the within subgroup frequency) may affect the Y and there are these other X's that will change at the between subgroup frequency (using just 2 layers of a sampling tree). I want to use sampling to help identify which sources are bigger (have greater leverage) because I want to know where to focus my efforts. But before I compare the sources I want to ensure the basis for comparison (the within subgroup) is stable (comparisons to an unstable basis is irrational). That is the purpose of the range chart. If the within subgroup sources are not stable, investigate why and take appropriate action (which may be to change the process). If they are stable, then proceed with the comparison.

Of course it is your choice how you "manipulate" your data. And my guess is JMP will be happy to help you manipulate the data. It seems to me your case is quite special. I don't think JMP should change the "software", a common cause action, to react to a special cause event.

Deming "Out of the Crisis", p.318:

Two kinds of mistakes:

1. Ascribe a variation or a mistake to a special cause when in fact the cause belongs to the system (common cause),

2. Ascribe a variation or a mistake to the system (common cause) when in fact the cause was special