Subgroups in Capability Analysis
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 This topic has 5 replies, 6 voices, and was last updated 17 years, 11 months ago by Andy Urquhart.

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December 3, 2003 at 4:32 pm #34010
I’m looking at data that is collected on a pershift basis. For conducting a capability analysis, I have an option to use subgroups. When using a value of 1 (individual observations) or a value of 3 (for 3 shifts), the numbers generated do not change. Could someone please explain how the subgroups work? I thought it has to do with making individual observations but when I think about it, I’m struggling with truly understanding how this works. Any help is appreciated!
Thank you!
JasonD0December 11, 2003 at 5:50 pm #93499
Kim NilesParticipant@Kniles Include @Kniles in your post and this person will
be notified via email.Dear Jason:
Since no one else has commented, Ill throw in my 2 cents worth but take it with a grain of salt as its not within my area of expertise.
Subgroups work via the central limit theorem in that they dont affect statistical confidence for most statements formed from groups of those types of measurements, only the measurement accuracy assuming that the underlying distribution is not perfectly normal.
Regarding selecting subgroups, thats really a different subject that depends upon what you want to understand / measure and how nonnormal you think the data might be. Using subgroups of three (one per shift in your case) would have the effect of normalizing the overall process and give you the best overall accuracy for any general statements you might form around your process CpK. However, what if one shift is producing more problems than another? In practical terms, as I understand your situation, if you suspect that your data does form a normal distribution, you might be better off forming and comparing three different CpK values, made from individual points, one for each shift.
I hope that helps.
KN http://www.KimNiles.com – https://www.isixsigma.com/library/bio/kniles.asp0December 11, 2003 at 10:28 pm #93506
Gerry MurphyParticipant@GerryMurphy Include @GerryMurphy in your post and this person will
be notified via email.I have come across this before.
3 shifts onfen operats as 3 completely different processes. Consider each individually. Compare the process averages and variation. this will point the way to where the improvement opportunities lie.
One shift could be running the plant flat out. High average production, the next shift picks up the pieces and has to do a lot of Repairs & Maintenance, the middle shift has then to adjust everything to get back on track for the cowboys on the first shift to reap the benefit!!!
Solution – train, redeploy etc the coyboys. Output and quality goes up as the differences between the shifts are significantly reduced.
Gerry0December 11, 2003 at 11:24 pm #93507It seems to me that some confusion is caused by 2 distinctly different uses of the term “subgroup” that often appear in the one discussion without being distinguished.
1. A subgroup can be used when collecting data, with the average of n individual readings from the same process being used in the later calculations.
This can help to meet the normallity requirement of many statistical tools (see below).
2. The output being studied can be divided into subgroups to analyse contributions from multiple processes. eg Each shift may have different parameters that effectively makes them different processes with different capability.
The subgroups in Jason’s question seem to be the first kind. I presume software is being used – it may assume that the values are already subgroup averages of n readings, or treat the input as raw data that it averages in subgroups of size n. Check out the formula in the manual to see what is happening. In any case I think the number of shifts is incidental to the calculation.
Also check out the Article Archives for some good reading – see under Quick Access on left of the screen. These are a few I found that might help:
Make Valid Control Chart and Subgroup Assumptions
– the section Control Charts Subgrouping By Machine Nozzle has a great example of the 2 uses of subgroup being intertwined.
Should You Use A Mean Or Individuals Control Chart?
Are You Sure Your Data Is Normal?
– Page 3 > Methods For Handling NonNormal Data0December 12, 2003 at 2:10 am #93514
Jonathon L. AndellParticipant@JonathonL.Andell Include @JonathonL.Andell in your post and this person will
be notified via email.The trouble with subgroups is that we try to anticipate which sampling scheme will tell us what we want to know, before we have gathered the data which contains the real answers. I would advise you to consider a sampling plan called Multivari on a trial basis. It will tell you a lot about what subgroup scheme you should use as you go forward. Good hunting.
0December 12, 2003 at 7:53 am #93520
Andy UrquhartParticipant@AndyUrquhart Include @AndyUrquhart in your post and this person will
be notified via email.I agree with Jonathon because Cp and Cpk are ‘individual’ metrics by definition. Many years ago I used to calculate Cp and Cpk indirectly from Shewhart Charts. This used to confuse the poor production manager because a low Cpk implies that some parts had been made out of tolerance, which was not the case. (The data came from a multinormal distribution!) Remember, much of statistical theory assumes random independence, homogeneity (equal variance) and normality, which is often not the case. The great advantage of the Austin Motorola Multivari chart was that it provided both univariate and multivariate analysis.
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