I was wondering when this would come up.

This has always caused me confusion as well - which one is long term? which one is short term? And then, the calculations themselves......

And the problem is, depending on which Google result you click first, you get a different description.

First - the k's. In both, Cpk and Ppk are like Cp and Pp EXCEPT they take centering into effect. What I mean is, in both indices, if the process is centered, then Cpk = Cp and Ppk = Pp. So the maximum they can be is the overall statistic. To me that's clear. the sub_ks are centering indices, the parents are variance.

Now, let's talk Cp and Pp then. We know they measure "fit". They are the same index, but one is called "short term" and the other "long term."

Both are expressed as (total tolerance) / (6 * sigma) so what's the difference between the two? Well, the difference is in the sigma.

When conducting the study, one takes subgroups. 3, 5, 6 doesn't matter. You are taking subgroups of size n and you do this N times. So your total number of parts you measure is n*N. Some people want 30. Some 100.

Let's look at the sigma.

In the Pp version, sigma is what Excel would give you if you asked for STDEV of all the measurements. In other words, it is the sigma for the n*N parts, regardless of subgroup. The whole sample.

In the Cp version, you are calculating the sigma for each subgroup, then averaging all these up (basically).

So here's the thought experiment..... Let's say take a subgroup of 3 and do this twice. My first subgroup have very little variation and I am near my lower limit. Then, I wait a while. Weeks. My second subgroup ALSO has little variation, just like the first, BUT ... my process has drifted due to tool wear and I am near the upper limit.

In other words 3 close together near the low limit, then 3 close together near the upper limit.

If I calculate Pp, my sigma will be big, because my "spread" will encompass most of my tolerance. And, since it is the denominator, my Pp will be low.

If I calculate Cp, my sigma will not be so big. Because I'm going to calculate it on subgroup 1 (very small), then separately calculate it on subgroup 2 (also very small) and average them. Resulting in a small variation. And, my Cp will be high.

Think about it - Cp is excluding subgroup to subgroup variation. It is only looking at within subgroup variation, which is then averages across all the subgroups. This is a SHORT TERM look at things. How noisy is it in and around a few parts, basically excluding drift (a long term effect).

Then Pp is LONG term. It maps out more of the variation in a long term effect.

Because of this TYPICALLY Cp > Pp and Cpk > Ppk. This is not ALWAYS the case, but normally it is.

Leastwise, that's what makes sense to me from looking at how we arrive at the numbers, regardless of what the internet tells me.