Ppk & Cpk - Within Subgroup Variation is always smaller than Total Variation?

[Stevenli]

There are a lot of thread to discuss the Cpk and Ppk, short-long vs. long term, or in other words within subgroup varaiation vs. total variation. My question is within subgroup variation is always smaller than total varation, so the Ppk is smaller than Cpk in Minitab. Is this true? I have run a case in Mintab that Cpk is smaller than Ppk. I am confused that how it comes.

Does anyone have some good ideas of that?

Thanks a lot.

Best Regards
Steven

[Darius]

Well in "Advanced topics on SPC" Don Wheeler said that this can be the case (ppk<Cpk) if there is wrong sample grouping, I can fire out a case, if there is a small difference between them (aka almost equal values), remember that this variation estimates are only that "estimates", so the possible variation on that estimate can produce this effect (ppk<Cpk), but in reallity are just the same value.

Total Variation = Within Variation + between variation + trend Variation

[Bev D]

yes within subgroup variation is always less than total variation, so Ppk will be less than Cpk for the same dataset.

Ppk can be mathematically greater than Cpk IF you have chunky data AND particularly if you are using the Range method of estimating the datandard deviation.

If you post your data set, we can provide a specific answer