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Ppk vs sample capability

Neo

I am comparing sample (or "short term") capability vs overall (or "long term") capability for several processes for my data set (cannot share), using JMP. I find that for some processes, the overall Ppk is smaller than the lowest sample capability. To give an example with reference to the picture below, for some processes, JMP gives me a Ppk smaller than 1.33 which is lowest capability for a sample (blue distribution's below) for a given process. Intuitively, this does not make sense to me, but is this possible (mathematically?), if yes, under what circumstances? If not, where could I be going wrong with my JMP analysis?

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All comments

jthi

What are you using as your subgroup in Cpk calculation?

Neo

@jthi I believe, each sample capability is calculated (JSL with example data here) using its own distribution i.e. the blue curves in each case, in the above example.

WebDesignesCrow

For me, I always look for Ppk.

Ppk value based on overall standard deviation of the data (same with std. deviation that you see in Distribution platform).

Cpk value varies depends on "estimated sigma" method based on subgroup sample size.

There's no way your process improvement can change the d2 constant of the subgroup sample size in Cpk calculation.

I think in JMP, the default of "estimated sigma" for Cpk is "average moving-range".

You can see the "within sigma" notes.

jthi

These are just much more generic comments.

If I remember correctly STIPS has good lesson about rational subgrouping https://www.jmp.com/en_fi/online-statistics-course/quality-methods.html .

Also

https://www.jmp.com/support/help/en/18.0/index.shtml#page/jmp/overview-of-the-process-capability-platform.shtml

hogi

what is the name of the other guy?
https://blog.minitab.com/en/process-capability-statistics-cpk-vs-ppk

Byron_JMP

Andrew Ridgeley!

oops, just labeled my decade...

shampton82

Hey @Neo ,

They way I was taught was that since Cpk is trying to estimate a short term stdev when using an I-MR (where as Ppk actually uses a stdev calculation) that it can sometime estimate it in a way that will give a slightly lower capability than the Ppk. This is just a mathematical anomaly and I always default to reporting the Ppk when Cpk is lower (usually they are pretty darn close though and not worth worrying about). Overall, I just default to Ppk and only worry about Cpk if someone is concerned about where our process could be if we could removed between subgroup variation.

Steve

Neo

@shampton82 Thanks.

My testing so far indicates that there is a possibility of a mathematical anomaly. I would like to push into this anomaly. Could I request a link (or links) to the background math used so that I can track down this anomaly?

Just to reiterate, that the Cpk discussed here is for a individual samples while the Ppk is for all the samples together i.e. overall capability. In my data, for some processes, I am getting overall capability (Ppk) lower than the lowest sample capability.

This discrepancy remains if I ask JMP to calculate Cpk (via within sigma capability summary) instead of Ppk or vice versa. The Cpk's are actually pretty close to the Ppk's so I do not think the discrepancy I am observing is stemming from the different ways of calculating sigma, rather my data.

I have used this script to check if I can reproduce the discrepancy with JMPs sample data but this does not show up for any process in the sample data.

shampton82

Try starting here:

Statistical Details for Variation Statistics (jmp.com)