Normal vs. When a Between / Within Capability analysis should be used?

D

davis007

#1
When should a Between / Within Capability analysis be used? Just exactly what is between / within Capability analysis? From what I can see the process spread is calculated both within each subgroup and between the means of each subgroup, a ratio of these values is then used to indicate the process spread for Cp etc. calculations. Why would I do this? I can some what see the usefullness of comparing the between and the within std dev to gauge if the process is in control or if the choice of subgroups is rational. But something tells me it is more complicated than that.

In any case any information is appreciated.
 
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C

caspar

#2
From a Minitab stat guide laying around

~~~
MINITAB’s capability commands
- Capability Analysis (Normal) draws a capability histogram of the individual measurements overlaid with normal curves based on the process mean and standard deviation. This graph helps you make a visual assessment of the assumption of normality. The report also includes a table of process capability statistics, including both within and overall statistics.

- Capability Analysis (Between/Within) draws a capability histogram of the individual measurements overlaid with normal curves, which helps you make a visual assessment of the assumption of normality. Use this analysis for subgroup data in which there is a strong between-subgroup source of variation, in addition to the within-subgroup variation. The report also includes a table of between/within and overall process capability statistics.
~~~
and...
~~~
Between-subgroup and within-subgroup variation

When you collect samples for control charts, you should select logical subgroups so that all the variation due to common causes is reflected in each subgroup. However, this is not always possible or practical.

For example, you may produce a large number of parts from the same batch or lot of raw materials. If each subgroup is sampled from a separate batch, then the within-subgroup variation will not account for the variation between batches. The between-subgroup variation needs to be estimated separately. The between-subgroup and within-subgroup variations can then be combined to reflect the total effect of common-cause variation.
~~~
 
D

davis007

#3
HMMM: Sorry to be dense but I am still not quite sure that I understand when it is appropriate to use the within between analysis.

As I understand it:
The within subgroup variation is the pooled standard deviation of the subgroups. The Cp and Cpk values are therefore representative of what the process could achieve. (All Between subgroup variability removed?)

The overall variation is the std deviation of all the samples. The Pp and Ppk is representative of how the process is actually performing.

If the Cp and Pp values are significantly different it could be due to variability between subgroups, in which case the choice of subgroups "may" not have been the best. However, if the choice of subgroups is rational “meaningful?” then the between subgroup variation needs to be calculated and used to modify the within subgroup variation to get the "true" potential capability of the process?

In my case I have measured the thickness at various points along reels of film. Cutting a wider piece of film into narrow strips produces these reels. Each piece of wide film is a considered a lot of film. When I do a capability analysis of the results I get a different Cp and Cpk depending on which subgrouping I use; Lot, Reel, Point along film at which the thickness is measured. If I use lot or Reel the Cp and Pp values are quite different, indicating that there is Reel to Reel or Lot to Lot variability. When I use point along the film at which the measurement is made as the subgroup the Pp and Cp values agree. So to find out what the potential capability of my process is I need to account for this in between group variability.

If this is correct so far my question is when do I use Between / within and when do I just change the subgroups? Does any of this really matter to a customer? Wouldn’t they just care about Ppk, how the process is actual performing?
 

Miner

Forum Moderator
Staff member
Admin
#4
davis007 said:
In my case I have measured the thickness at various points along reels of film. Cutting a wider piece of film into narrow strips produces these reels. Each piece of wide film is a considered a lot of film. When I do a capability analysis of the results I get a different Cp and Cpk depending on which subgrouping I use; Lot, Reel, Point along film at which the thickness is measured. If I use lot or Reel the Cp and Pp values are quite different, indicating that there is Reel to Reel or Lot to Lot variability. When I use point along the film at which the measurement is made as the subgroup the Pp and Cp values agree. So to find out what the potential capability of my process is I need to account for this in between group variability.
This description of your process is very helpful because you have a lot of sources of variation occuring together. You must identify each and choose your rational subgroups carefully.

You will probably have one source of variation that acts across the wide roll that could be caused by such things as non-parallel, tapered, barrel/hourglass-shaped rolls. When you cut the reels into smaller ones they may appear as if they were from different process streams

If you check consecutive linear points in one location, you might see one of two things: 1) pulsating variations from out-of-round rolls, or 2)autocorrelation, where it changes very slowly over time.

If your charts show extremely tight limits around what appears to be normal variation in the average, it could be due to the affect of autocorrelation. In this case you can test for autocorrelation and adjust the time between individual samples to the time when the effect of autocorrelation disappears.

From your process description, I would consider using an I-MR chart with the period between samples set based on the autocorrelation test. For a short time I would also run parallel I-MR charts on both sides and the middle of the roll to verify across the roll consistency.

The charts will provide more useful information than the between/within Ppk/Cpk because you will know exactly where the variation is coming from.
 
D

davis007

#5
Miner:

Thanks for the advice. I will / am using control charts to try and identify the source of the variation. I understand that they contain much more information than single value measurements of a process. As you have noted there is variation both across the roll and from lot to lot.

However, I am being asked to provid an estimate of the current capability of the process. Depending on what sub grouping I use I can get a Cp value from 0.88 to 1.05. (All the while obtaing a Ppk of 0.10) What should I report???? If I use Between / Within I can get yet another set of Cp values. If it were just a case of a few percentage differnce I would pick one and live with it but 0.10 to 1.05 is quite a range to choose from. It seems that what you use should depend on how the data was collected and what the information is to be used for.

As the data is to be used to gauge our ability to produce this film to spec. , which without some serious improvement efforts is going to be an impossible task, I am leaning to reporting the very low Ppk value. This might give managment some imputus to start planning some much needed capital improvments.
 

Statistical Steven

Statistician
Staff member
Super Moderator
#6
I think this thread is discussing different concepts about sources of variation. There are 3 sources we can quantify, within subgroup variation (tracked on a control chart), between subgroup variation and total variation which is the sum of the two. An assumption of control charting is that the variation seen within a subgroup is indicative of the short term process variation, and is therefore used to compute the control limits of the Xbar chart (or X chart). When you talk about Cp or Cpk I would suggest you use the total variation (within and between combined) since it gives the best estimate of the long term variation. Of course, this will give a lower Cp or Cpk value. Inherently, this is what is wrong with these indices, the estimate of sigma is open to intepretation.
 

Miner

Forum Moderator
Staff member
Admin
#7
davis007 said:
However, I am being asked to provid an estimate of the current capability of the process. Depending on what sub grouping I use I can get a Cp value from 0.88 to 1.05. (All the while obtaing a Ppk of 0.10) What should I report???? If I use Between / Within I can get yet another set of Cp values. If it were just a case of a few percentage differnce I would pick one and live with it but 0.10 to 1.05 is quite a range to choose from. It seems that what you use should depend on how the data was collected and what the information is to be used for.

As the data is to be used to gauge our ability to produce this film to spec. , which without some serious improvement efforts is going to be an impossible task, I am leaning to reporting the very low Ppk value. This might give managment some imputus to start planning some much needed capital improvments.
As Statistical Steven pointed out the measure that uses the total variation is the truest measure of your process capability. Although it is not the sum of the standard deviations but the sum of the variances. Variance(total) = variance(between) + variance(within) [variance = (StdDev)^2].

Not wanting to assume anything, do you understand the difference between Pp and Ppk? Cpk and Ppk are influenced by the centering of the process to the middle of the spec. Cp and Pp are not. This is the reason you have a Ppk of .10 and Cp of .88 - 1.05. You did not say what your Pp or Cpk were. I presume the Pp was in the Cp ballpark.

You can make an immediate improvement in the Ppk by centering the process. That will make Ppk very close to the Pp. After that you must reduce the variation from the other sources that we discussed earlier.
 
D

davis007

#8
Miner and others:

Thanks for further information. Yes I did, at least somewhat, understand the difference between Pp and Ppk and Cp and Cpk. I have pulled the equations from Minitab’s web site and this shed some light on the differences. And yes one big issue at this point is that the process is not centered, so the Pp and Cp are much higher than the Ppk an Cpk. The other issue and the original reason for my post was that there is a difference between the Cp and Pp that depends on what I use as a subgroup in the analysis.

If I use a subgroup of reel, the Cp is 1.05 but the Pp is 0.59. If I use distance along the reel at which the data is taken. The Cp is ~0.6 and the Pp of course is still 0.59. So it seemed to me that this was an indication that there was some effect of reel-to-reel variation. Thus the questions 1.Should I somehow take into account this between reel variation? 2. Is the "correct" way to do this between / within analysis?

The more I read this forum and the responses to my questions the more I am of the opinion that the Pp and Ppk values are representative of what the customer would see when he looks at our product. The ultimate goal is to have a process that is capable of "pleasing" the customer by meeting his/her expectations. The Cp and Cpk, between / within analysis, choice of subgroup, DOE etc are useful tools in finding the source of variation that can be targeted for improvement projects.

Again thank you all for your help. This forum has been valuable to me both by reading posts to gain exposure to the issues and techniques and posting questions for clarification and help with specific issues.
 

Miner

Forum Moderator
Staff member
Admin
#9
davis007 said:
The other issue and the original reason for my post was that there is a difference between the Cp and Pp that depends on what I use as a subgroup in the analysis.

If I use a subgroup of reel, the Cp is 1.05 but the Pp is 0.59. If I use distance along the reel at which the data is taken. The Cp is ~0.6 and the Pp of course is still 0.59. So it seemed to me that this was an indication that there was some effect of reel-to-reel variation. Thus the questions 1.Should I somehow take into account this between reel variation? 2. Is the "correct" way to do this between / within analysis?
If subgroup of reel means each individual reading is a different reel, and the other subgroup is each reading is separated by distance on the same reel, this is an indication that the major source of variation is distance down the reel because short term variation (capability) down the reel equals long term variation. Depending on how you sampled your reels, the variation across the role is not a major source of variation because the short term variation is much less than long term variation. The long term variation arises from the within reel distance variation.

davis007 said:
The more I read this forum and the responses to my questions the more I am of the opinion that the Pp and Ppk values are representative of what the customer would see when he looks at our product. The ultimate goal is to have a process that is capable of "pleasing" the customer by meeting his/her expectations. The Cp and Cpk, between / within analysis, choice of subgroup, DOE etc are useful tools in finding the source of variation that can be targeted for improvement projects.
In this scenario the Pp/Ppk is what the customer will actually see and what should be reported. Centering the process will maximize Ppk to Pp the fastest. The next step is to raise Pp to the Cp level of 1.05 by reducing within reel variation.

I suggest a sampling plan that measures an individual reel at distances small enough to pick up potential cycles caused by the equipment. For example, if you are calendaring the film, measure at distances that will give you multiple measures within the circumference of the calendar roll (such as every 45 or 90 degrees). and continue for multiple rotations of the roll. Plot the points on a run or I-MR chart and look for periodicity. The wavelength of the periodicity should point toward a likely suspect.
 
D

demian

#10
Hi all. It might be late but the problem seems to be still unsolved. I read all these comments and also the Minitab help but it gets even more confusing while I'm trying to calculate the indices myself. Minitab help says "When calculating Ppk, Minitab estimates s-overall considering the variation both within and between subgroups" but as far as I remember first of all s-overall is not an estimation; it's calculated for the whole data. Second it doesn't represent between plus within variation but s-total does (Total variance = between variance + within variance).
I also saw a difference between the stdev that is shown on "Capability Analysis" results sheet and that of what I calculated with the calculator of minitab itself. For example for the camshaft.mtw (which is among examples of minitab itself) I calculated stdev for the Lenght column to be 1.335 (I checked this by calculating xi-mean manually too). But the capability study shows a 1.338 stdev which I can't figure out how it is derived.
I wanted to know if I could find out how the stdev is calculated for within and between subgroups either. I found means for the 20 groups (subgroup size of 5) and calculated the stdev for these 20 means (I thought it would be something like the ANOVA method). The result was 0.76937 which was neither 0.35257 (between stdev) nor 1.22964 (within stdev).
Does anyone know how these stdevs are calculated?
 
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