topic Re: How are Avg Rs for XBarR-Charts with subgroups of varying size calculated ? in Discussions

How are Avg Rs for XBarR-Charts with subgroups of varying size calculated ?

UnivariateRules — Fri, 16 Jun 2023 11:18:14 GMT

Hello

When I create an Xbar Chart with sub groups of various sizes defined by a label, I am getting different Avg Rs for the different subgroups (see graph).

How exactly are the avg Rs (displayed in the R Chart as the Center line) for a given subgroup calculated ?

Originally I thought they were the mean of the ranges within a subgroup, but there are several occasions (in the graph below), where the Avg R is bigger than the Range within a subgroup, so there seems to be another method behind it.

The used data is a color measurement with the subgroups chosen according to the film build the color layer has. (I am working with JMP 17, but have the same question with JMP 16)

thank you and best regards

Re: How are Avg Rs for XBarR-Charts with subgroups of varying size calculated ?

statman — Fri, 16 Jun 2023 18:01:55 GMT

First question, why would you want subgroups of varying size? This changes the causal structure within subgroups (the opportunities for x's to change) and therefore changes the utility of the control chart. The range chart answers the question: Is the variation within subgroup consistent and stable? The only way to answer this question is to compare something to itself over time. If you change the comparisons over time, you no longer are able to answer the question regarding stability and consistency. In addition, any comparison to the between subgroup variation (X-bar charts for example), is no longer useful.

Regarding the technical question of calculations, those averages are over multiple within subgroup ranges, so there will be within subgroup ranges above and below that average. I have attached your data set with the ranges calculated for each varying subgroup. These are the plotted values on your chart.

Re: How are Avg Rs for XBarR-Charts with subgroups of varying size calculated ?

WebDesignesCrow — Mon, 19 Jun 2023 04:06:04 GMT

The centerline for R subgroup is an estimate of R at ith.

The dot is the R value for the subgroup.

You can refer here:

https://www.jmp.com/support/help/en/17.0/#page/jmp/statistical-details-for-xbar-and-r-charts.shtml#

Looking at your data, some subgroups data (like int f.b for 50 does not have mean or range, since it only has 1 measurement).

Not sure what is your objective of using the X-bar, Range control chart.

Re: How are Avg Rs for XBarR-Charts with subgroups of varying size calculated ?

UnivariateRules — Mon, 19 Jun 2023 05:46:19 GMT

I am aware, that I used the Control Charts kind of unconventionally. It seemed like a possible tool to determine the film build where color stability is achieved. It still might be an inappropriate tool, but your answer already helped a lot. Thank you.

Re: How are Avg Rs for XBarR-Charts with subgroups of varying size calculated ?

UnivariateRules — Mon, 19 Jun 2023 05:52:34 GMT

I was not quite sure, if I used the Xbar Chart only unconventionally or wrong (with your and the answer of WebDesignsCrow I am still tending towards unconventionally). I wanted to determine, if the Chart would be a suitable tool to determine which film build is necessary to achieve color stability on a panel. I choose my subgroups according to points on a panel which have a given film build. The numbers of those points on a panels is determined by the process and I have only very limited influence on that.

Thank you very much for your reply, it helped.