# Capability Analysis for Normal Data

Six Sigma – iSixSigma Forums Old Forums General Capability Analysis for Normal Data

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• #35648

CT
Participant

When performing Capability Analysis – Normal in Minitab, am I correct in assuming that I should use only the Overall Capability (Pp and Ppk) versus the Within Capability (Cp and Cpk) when my subgroup size is one.

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#100744

Gabriel
Participant

No. As with any other subgroup size, you can use Cp/Cpk, Pp/Ppk or both, depending on what you want to know.

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#100752

CT
Participant

OK, so now what? I thought I understood the difference between “within” and “overall,” but now I think I am more confused. I thought that if my subgroup size were 1, that these would be nearly, if not, identical? Maybe you can do better job of explanining the difference – in laymans terms – I know a fair amount about statistics, but I am not a statistician. Thanks for your help.

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#100768

Gabriel
Participant

Give me your e-mail, I’ll send you an example.

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#100769

CT
Participant

[email protected]
Thanks!

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#100776

GAC
Participant

I’ll get your back on this one Gabriel.  Pp/Ppk, and Cp/Cpk are actually identifcations of two different things.  So, the subgroup size is irrelevant.  In fact, if the subgroups are representative of similar process outcomes, separated only by units of time, the between subgroups value is more important (in most instances) than overall.  So, Cpk will always be relevant, while Ppk may not be.
GAC

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#100786

Gabriel
Participant

“In fact, if the subgroups are representative of similar process outcomes, separated only by units of time, the between subgroups value is more important (in most instances) than overall.”
In which way? Example?
“So, Cpk will always be relevant, while Ppk may not be.”
In which way? Example? How does this last sentence relates with the first one (the seem to be saying the opposite thing).
For the record, I don’t agree with these two sentences, so go get someone’s else back :-)

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#100839

Sean
Member

Gabriel,
Thanks for providing the spreadsheet.  I worked through it and it was very useful and informative, however I am still having trouble with this concept.
I understand the formulaic differences between Cp/CpK and Pp/Ppk, however I am having trouble grasping the concept of within vs. overall variation/sigma/capability for a subgroup of size 1.  How can there be any variation within the subgroup when the subgroup has only one data point.
Regards, Sean

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#100841

Mikel
Member

When you have a subgroup size of 1, moving range is used as a surrogate for the within group variation. Go look at the explanation of an I-MR chart.

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#100842

Sean
Member

Yes I understand how it is calculated, just not why.  Or more accurately I don’t understand why that is considered a measure of “within subgroup” variation.  Perhaps it is just the terminology that I’m confused about…
SP

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#100859

Gabriel
Participant

Sean,
Let’s try to clarify this.
An individual values / moving range chart is, in fact, two charts: The individual values chart and the moving range chart.
In the individual values chart, the subgroup size is 1, as you said.
But in the moving range chart, the subgroup size is 2, not 1. Do you have a table of constants for SPC? Go compare the constants d2 and D4 used in an IX-MR chart with those used in a Xbar-R chart for n=2. They are the same figures.
Now, is it valid to consider two consecutives individual value points as 1 subgroup for the MR chart? Let’s review the concept of rational subgroup.
Ideally, one would like have complete information about the distribution a process is delivering at given instants, as one wants to compare the distributions delivered at different instants to check if they are the same (stable process) or has changed (unstable process).
The problem is, the process does not delivers “a distribution” in one instant. It delivers 1 value at a time. So one take a sample of a few values that are as close in time as possible, called “rational subgroup”, and pretend that this subgroup is a snapshot of “one instant” in the process (it is not, because the values within a subgroup were produced at different instants, close one from the other but not the same instant).
By definition, a rational subgroup is “A subgroup gathered in such a manner as to give maximum chance for the measurements to be alike and the maximum chance for the subgroups to differ one from the other. This subgrouping schemme assumes a desire to determine whether or not a process’s variation appears to come from a constant system of chance causes” (Statistical Process Control – Ford, Chrysler, GM).
Or, the one I like more, “A rational subgroup is a sample intended to repressent one instant of a process, in such a way that the chances that the subgroup is affected by common causes of variation only are maximized and hence, at the same time, the chances that any variation due to special cause happens only between subgroups (and not within) are maximized too. The way to do this is to take the parts for each subgroup as close as possible in time one from the other.” (Just invented – Gabriel).
Typically, when you use an Xbar-R chart, consecutive parts are used for the subgroup. This is already imperfect as a rational subgroup because even “consecutive” is not “one instant”. Sometimes, even consecutive is not possible (for example because of a production rate that is faster than the sample colection rate) but the parts are anyway very close in time. It is a little more imperfect, but it is still close. In both cases, note that wat you did was “to take them as close as possible” to, given the available resources, “give maximum chance off…(etc)..”, allways with the intention that the subgroup represents one instant of the process” motivated by a “desire to determine if the variation is due to common causes only”. So, in any case, you took the best rational subgroup you could with the available resources to do that.
Now, let’s say that you decided to use an IX-MR chart insteed. Why did you decide to do that, when you could have gone for an Xbar-R? Whatever the constraint is (time, cost of measurement, destructive test, …), the best you can do in this context to take the parts as close as possible is to take two consecutive individual values (not two consecutive parts from the process, but two consecutive individual value points from the chart). It is more imperfect than before, but it is still the best you can do with the resources avalilable and the “intentions” and “desires” are the same, so it is still the best rational subgroup you can take. If not, you would have gone for an Xbar-R chart.
Now, a variation due to special causes tha happen between two individual values, happens “btewen subgroups” or “within the subgroup”? The answer is: both. An the answer is the same whetet rou are using individual values or subgroup averages. If a special cause happens to appear just in the midlle when you are taking the sample for one subgroup, this variation will be reflected in the between subgroups variation (that’s Ok, because you want it to include variation due to special causes) and in the within subgroup variation (that’s not nice, because one wants the within subgroup varaiton to reflect the variation due to special causes only). Of course, while the chances that a special cause appears just in the middle of a few consecutive parts is minimal, it is 100% sure that any special cause woll happen within some subgroup in an individuals chart.
But, not all are bad news. Here you have a good one: A special cause of variation, no matter where it happens, affects the overall between subgroup variation. If this speciall cause happens within a subgroup, then only the variation within that subgroup will be affected, but as the estimation of the within subgroup variation is an average of the variation within each subgroup, one outlier will not make a big difference.
Imagine a case where, in the middle of the chart, the process has a big shift up in the average. All subgroup before this shift will have values that are significantly lower than all values after the shift. When you compute the overall standard deviation, all values are far from the grand average and then the resultant total variation is large. However, the variation within the subgroups is the same with or woithout the shift exept, maybe (or for sure in the case of individuals charts), in the only subgroup within which the big shift happened. If you had 50 subgroups, 49 of them have the same “within” variation with or without the shift, and only one is “inflated” by the shift. So the within subgropup variation, which is the average of all the subgroup variation, is not much affectd by the shift.
Another example. Imagine a process that, due to some special cuase, drifts 3mm along the 50 individual values in the IX-MR chart, in a process where the standard deviation when stable is only 1mm. The effect of this special cause between consecutive subgroups (which is within subgroup in the individuals chart) is 0.06mm (3mm/50), negligible compared with the 1mm standard deviation of the stable process, so the within subgroup variation will not be practically affected. On the other hand, when you compute the total variation you will be comparing some subgroups that are 3mm appart. The total variation computation does not take into account whether the subgroups that are different from the average are consecutive or not. 1,2,3,4,5,6,7,8,9 will have the same total variation, but much less within subgrouop variation, than 1,5,7,6,2,8,3,9,4.
There is just one thing to care about: As long as you have smooth drifts or isolated shifts, there is no problem in computing the “within subgroup” variation from the range in consecutive points of the individuals chart. But if your process is chaos and you have sifts and drifts that appear and disappear between most individaul value points, then the IX-MR chart cannot distinguish between the between subgrop and the within subgroup variation, because the approximation that isolated increases in a few moving ranges (isolated shifts) or very small increases in all moving range (smooth drifts) do not affect too much the overall average moving range would not be valid is significant shifts happen between about all values.

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#100874

Hariharan
Participant

Gabriel, thanks for another detailed answer.   It was explained well.   I finally understood it.  If you don’t mind me asking, what is your background?

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#100906

Sean
Member

Thanks Gabriel.  You had me convinced by the third paragraph, but the rest of the answer was interesting and helpful too!  You should write a textbook…
I only have some slective pieces of the standard SPC constants.  Can you recommend a single online source that I could go to find them?  If not then does the AIAG SPC Manual have them?
Regards, Sean

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#100907

hongkeat
Participant

Below is the link to Cpk/Ppk formulas and unbiasing constant, provided by Minitab.

Related Documents

Capability Analysis (Normal) Formulas (http://www.minitab.com/support/docs/CapaNormalFormulas.pdf PDF file)

Unbiasing Constants c4 d2 d3 d4 (http://www.minitab.com/support/docs/UnbiasingConstantsc4d2d3d4.pdf PDF file)

Unbiasing Constant c4 Prime (http://www.minitab.com/support/docs/UnbiasingConstantc4Prime.pdf PDF file)

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#100909

Savage
Participant

Donald Wheeler’s book has all the constants.  If you check out his site, I think you can order SPC cards that list all the constants and calculations.
I’m sure others will list more sources.

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#100917

Gabriel
Participant

And yes, AIAG’s SPC handbook has all constants for Xbar, median, IX, R, and MR charts for subgroup sizes up to 25.

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#100920

Gabriel
Participant

You mean education and working experience?
– Aeronautical engineer (there is no BS title in Argentina, it is a 6 years career).
– Post-graduate (like an MS) in Quality Engineerieng.
– 7 years working in Quality in 2 manufacturing companies.
– A constant need to understand the “why” behind the “how”. I don’t belive in recipes until I understand why they work.
Which of them had the greatest impact? The last one, by far.

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#112927

I’Anson
Participant

Gabriel,
Please Would you mind to send me the example? I have just started to know Minitab and I am little bit confused.
Thank!!

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