Difference between Cpk and Ppk

I took a webinar from minitab on SPC. During the webinar the instructor mentioned that the only difference between Cpk and Ppk was in the sigma calculation. std = Rbar/D* is used for Ppk while the normal calculation of STD ( sqrt of the sum of the difference between the data and the mean/(n-1) ) is used for Cpk. I thought those two calculations measured the standard deviation within the subgroup. Can anyone enlighten me?

7 Replies
Ajoy Basu
10 Posts

@Roger Tonneman

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Minitab uses stdev = Rbar/d2 only when subgroup size = 1.

For subgroup sizes > 1, the stdev formula is the very similar for Cpk and Ppk. It is the same if unbiasing corrections are ignored.

So, the only difference between these metrics is the ‘sources of variation’ included in your sample. If some sources of variation, the capability index is Cpk. If ‘all’ (or almost all), then the capability index is Ppk. Hope the figure helps.

@Roger Tonneman
Perhaps it's time to consider something other than capability indices such as Cpk and Ppk. A number of experts have advocated this over the years, as described in this article https://www.pyzdekinstitute.com/blog/continuous-improvement/its-time-to-ditch-process-capability-indices.html
I also listened to the Minitab SPC webinar. He did list both formulas you mentioned on one of his charts. You had the two formulas switched when assigning them to the Cpk and Ppk. Roger T's reply corrects
this. Tom P's reply (with link) is worth reading,
John Conte
5 Posts

@Roger Tonneman This discussion is way overdue. For twenty years I taught the ASQ CQE BoK that included Cpk and Ppk as topics. It was embarrassing to show the history of each and how various texts published by ASQ Press would treat this subject. But my favorite from the ASQ Certified Quality Inspector include the following:

Page 303, The Certified Quality Inspector Handbook, H. Fred Walker, Ahmad K. Elshennawy, Bhisham C. Gupta, and Mary McShane-Vaughn, ASQ Press 2009

“Kotz and Lovelace (1998,253) strongly argue against the use of Pp and Ppk. They have written:

We highly recommend against using these indices when the process is not in statistical control. Under these conditions, the P-numbers are meaningless with regard to process capability, have no tractable statistical properties, and infer nothing about long-term capability of the process. Worse

still, they provide no motivation to the user-companies to get their process in control. The P-numbers are a step backwards in the efforts to properly quantify process capability, and a step towards statistical terrorism in its undiluted form.

@Roger Tonneman this link to an old Minitab blog post is what I always fall back on when trying to understand/explain the difference between Cpk and Ppk.

https://blog.minitab.com/en/process-capability-statistics-cpk-vs-ppk

At the expense of hijacking this thread, I am interested in this idea that Cpk/Ppk are not useful indicies. I think that warrants more discussion. There's a nitty-gritty, detailed level to worry about, sure, but many organizations don't have the luxury of having a team of QEs to disect each statistical metric. For those organizations that have at least a basic understanding of the pros and cons of the metric, isn't it useful as a quick-and-dirty answer to either a) are we improving or b) are we focusing on the right areas for improvement?

Jay Arthur
27 Posts

@Roger Tonneman
People often misuse Pp/Ppk for Cp/Cpk. Pp/Ppk is for total populations. Cp/Cpk is for a sample of the total population. Your customer wants Cp/Cpk. I find it a waste of time to teach people all of the formulas. They are too complicated to do by hand. Buy some SPC software to get Cp/Cpk.

Depending on the subgroup size, sigma estimator (not stdev) can be calculated three different ways. Here's a short write up about the differences:

@Roger Tonneman

Thanks for asking. In theory the underlying difference between Cpk and Ppk is SUPPOSED TO BE whether we are observing "short term" or “long term” process variation. Unfortunately, no software formula is able to discern what number of samples differentiate between the two concepts for a specific process. As a result, we get numbers that rarely reflect the reality of the process in consideration, so the numbers do little to enlighten us about actual process variation. I would say use Cpk as an “order of magnitude” estimation of failure/defect rates, and don't sweat Ppk. More importantly, be SURE to view the data in a process behavior chart (some call it a control chart), and use your eyes and brain to learn about dynamic process variation.