Rational Subgroup and Estimation of Variability Due to Common Causes

B

Bapun

#1
Hi friends

I have joined the forum just today.

Wish you all a very bright & properous New year (2008)

I have been exposed to the field of SPC some time back.

I understand that the concept of Rational Subgroup and its use in estimation of variability due to chance causes is central in SPC

However the question which is bugging me is -

Within Rational Subgroup (RS) variation is assumed to capture the Common cause variation.

How to choose the RS in a particular situation which ensures that the assumption (that the RS realy captures the common Cause variation, nothing more and nothing less) is correct ?

I am unable to find a satisfactory answer to this question.

Please enlighten me on this point.

Thanks in Advance

Bapun

India
 
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Stijloor

Staff member
Super Moderator
#2
Hi friends

I have joined the forum just today.

Wish you all a very bright & properous New year (2008)

I have been exposed to the field of SPC some time back.

I understand that the concept of Rational Subgroup and its use in estimation of variability due to chance causes is central in SPC

However the question which is bugging me is -

Within Rational Subgroup (RS) variation is assumed to capture the Common cause variation.

How to choose the RS in a particular situation which ensures that the assumption (that the RS realy captures the common Cause variation, nothing more and nothing less) is correct ?

I am unable to find a satisfactory answer to this question.

Please enlighten me on this point.

Thanks in Advance

Bapun

India
Hello Bapun.

Welcome to The Cove! :bigwave: :bigwave:

Happy New Year to you.

A search on The Cove Forums revealed this.

Are you familiar with this great resource? This may help too.

Stijloor.
 

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#4
Establishing rational subgrouping requires knowledge of the process being monitored. To illustrate the issue, I think it best to give an example (we had something like this on the Cove as an actual data example a few years back).

Let us say that I am monitoring a production output, and I choose to subgroup in sequential lots of 5 units produced. Let us assume that there is something in the process that makes every 5th unit significantly smaller than the other four units. Since my subgroup is 5 units, every group will include 1 small item, and 4 regular sized items. My average size, and range of the size within each sample will be similar from group to group. I will then assume that any variation observed is "common cause" since the variability from group to group is stable and predictable.

But then, let us change the grouping size. Let's plot an individuals chart. When I do that, I will visually see that every fifth unit is different. Perhaps every fifth unit will be outside the control limits if the difference is severe enough. In this case, I will end up declaring the process to have "special cause" variation - every fifth unit is "different".

So, depending upon your grouping plan, one chart gave that there was common cause variation, the other said special cause. Interestingly, both interpretations could lead to improvement - if the common cause variation was "too high" and the process not capable in the first scenario, you would then look further into the data and discover the every fifth item issue. The special cause in the second scenario should immediately lead you to an answer.

I hope that illustration is of assistance.
 
B

Bapun

#5
Dear Frainds,

Extremely sorry for being late, I was busy because of serious illness of one of my family members and could not visit the forum.

Thanks to Stijloor. I have visited the links suggested by you. They are excellent. I need some time to critically look into them and then only I can comment on them.

Thanks to Brad for the links you have suggested I have seen them too. They will surely be helpful.

I am afraid; I was not able to put my question clearly. I would try to put it in a better way.

Rational Subgroup as a concept is excellent. They, IF selected correctly will surely give a good estimate of the common cause variation.

However It’s really a VERY BIG IF. The thumb rules like “five consecutive” pieces are supposed to form a Rational Subgroup (RS); however my question was how one can be sure that the selection was correct. Often one comes up with situations where one finds that the Control Chart shows unstableness.

This could be because the selected “Rational Subgroups” captured only a part of the Common cause variation (e.g. variation due to the measurment process only) and left out others. As a consequence Such a selection of Rational Subgroup would underestimate the common cause variation of the process.

It is important that the selected Rational Subgroup captures the entire common causes variation and excludes any variation due to special causes.

How one can be sure that this will be the case for a particular selection of a Rational Subgroup?

I thank Steve also for his posting. It was clear that he has understood my question. He gave a nice example to support his views.

My fresh question are

- whether one has to depend on his experience and develop one’s own method of selection of Rational Subgroups or is there or could there be a somewhat structured method for doing so?

- Can statistical methods provide some guidance in this regard ?


Regards,

Bapun
India
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#6
Dear Frainds,


My fresh question are

- whether one has to depend on his experience and develop one’s own method of selection of Rational Subgroups or is there or could there be a somewhat structured method for doing so?

- Can statistical methods provide some guidance in this regard ?


Regards,

Bapun
India
The only 'structured' way is to undertand your process, how variation could happen in time groupings (within piece, piece to piece, cavity to cavity, tiem to time, operator to operator, line to line or equipment to equipment, etc.), get some data across these groupings, plot it in time sequence and look at it. Rational subgroups are not assigned ahead of time - they are assigned only after knowledge of the true process variation is gained. Then the rational subgroup is determined to match the actual variation. That is why it is called rational.
 

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#7
My fresh question are

- whether one has to depend on his experience and develop one’s own method of selection of Rational Subgroups or is there or could there be a somewhat structured method for doing so?

- Can statistical methods provide some guidance in this regard ?


Regards,

Bapun
India
This is a case where there is not a silver bullet answer. Rational subgrouping requires knowledge of the process, and experience. Probably the most important "structured method" is to do the SPC itself correctly and then you will be able to detect problems with the subgrouping.

Personally, I prefer to do individuals charting. The weakness in this is less ability to detect shifts in the variation (standard deviation) of the data. The other potential weakness is that if you have A LOT of data (say from an automated measurement system) you may need to go to large subgroups to keep the chart size reasonable. In that case, I prefer xbar - sigma charting.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#8
yes - simply plotting your data in any time series chart will do the the trick. I personally prefer to plot my data with a multi vari chart. Of course if there is no within piece or within (fixture/mold) to be measured the multi-vari defaults to looking like an individuals chart...

but again teh message is that there is no "a priori" method.
 
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