Can you quote the mentioned sections for those of us who don’t have access to the documents?

Memorize the following:

Data that has a boundary condition cannot be expected to have a Normal distribution, especially if the boundary is the ideal target (flatness)

Normality has nothing to do with stability. Many stable processes are not Normal at all.

Normality has nothing to do with capability - except in a choice of distributional formula to ‘predict defect rate’ (a very flawed but incorrect application that is popular with some companies…)

In general theory for capability indices (Cpk and Pk, etc.) there can be no reliable prediction without stability.

The only difference between Ppk and Cpk (as Miner said) is that Cpk uses the within subgroup variation (sometimes called short term) and Ppk uses the SD of all of the data (within and between; aka long term, except in pre-reduction were the Ppk formula is used for short term estimate as there may not be enough production to have a useful subgrouping scheme)

I thought you can only predict capability indexes (Cpk and Ppk) with a normal distribution? You can transform the data or use another distribution model to calculate Cpk/Ppk such as in minitab but that would not give you as reliable results. Especially when transforming data so that it becomes normal, that reduces the usefulness of the capability indexes.

Regarding one sided specifications:

Per the AIAG manual:

"2.2.11.5 Processes With One-Sided Specifications or Non-Normal Distributions

The organization shall determine with the authorized customer representative alternative acceptance

criteria for processes with one-sided specifications or non-normal distributions.

NOTE: The above mentioned acceptance criteria (2.2.11.3) assume normality and a two-sided

specification (target in the center). When this is not true, using this analysis may result in

unreliable information. These alternate acceptance criteria could require a different type of index

or some method of transformation of the data. The focus should be on understanding the reasons for

the non-normality (e.g., is it stable over time?) and managing variation. Refer to the Statistical

Process Control reference manual

for further guidance."

Regarding stability, I thought that Ppk can still be calculated with an unstable process? As long as the instability is due to predictable causes. See AIAG manual:

"Initial Process Studies. The purpose of the initial process study is to understand the process

variation, not just to achieve a specific index value. When historical data are available or enough

initial data exist to plot a control chart (at least 100 individual samples), Cpk can be calculated

when the process is stable. Otherwise, for processes with known and predictable special causes and

output meeting specifications, Ppk should be used. When not enough data are available (< 100

samples) or there a sources of

variation, contact the authorized customer representative to develop a suitable plan."

I might be interpreting the manual incorrectly and drawing the wrong conclusions.