Given this formula Pp/Ppk is always less than Cp/Cpk because the total variation is always greater then the within subgroup variation. Even for a perfectly homogenous process as there will always be the subgroup to subgroup rumble….there is a rare condition (almost always due to a subgrouing or sample frequency problem and chunky data) where the within subgroup variation is greater then the long term variation and then Ppk will be less than Cpk…this is a signal that something is wrong. Because this is in fact how math works. The real world doesn’t do what math tells it to do, math describes what we think the ear world is doing. If the inputs to the mathematical formula are incorrect or flawed the output of the formula may be mathematically correct, but the answer is still wrong. There is a difference between real world process and theoretical math…it isn’t weird. In 40+ years I have never seen this occur in a real process except as an error as described above and even that has happened in less than 5 cases. In these cases the difference is quite small. I have been involved in a lot of processes in numerous industries with every scientific and engineering discipline except nuclear and civil…models do not generate real world data.

At first I thought that the OP made a simple mis statement when asking why Ppk was less than Cpk as this is what is supposed to happen. Long term variation is larger than short term/within subgroup variation there fore Ppk <Cpk. Then I thought maybe the OP was thinking about just the SD and not the actual Ppk/Cpk indices but the OP has failed to clarify this.

Was the statement to look at the formula harsh? Sure after numerous times asking the clarifying questions and getting zero response for a question that has been asked and answered here for 3+ decades you tend to get frustrated. If someone doesn’t even get the basics we must address the basics first or the Answer to the more complex question won’t make sense. After 30 years on this forum, and 45 years in industry I know that the question the OP posts is often not the real question. There is usually something left out that is the key to the OPs confusion. This is why those who have been here a long time and who have a lot of real world experience ask questions before giving answers.

So I ask the OP to clarify the central question.

As for posting articles for members to read I and others do that frequently as (1) why should I write a book in my response when someone else provides a well written response and (2) those who are new to a complex discipline like Quality Engineering need to learn how to do their own research and where to find it. Additional resources for learning should always be welcome. I did make my point regarding outlier testing; twice. Then I posted 2 references that provide independent and additional insight into outlier testing. What exactly is wrong with that??? We are not here to provide in depth complex training; we are here to answer specific questions. Remember this is a free forum.