without stability the Cpk is meaningless but I cannot convince management of this.
Maybe I will say something that many won't be agree but..
Management thinker Peter Drucker is often quoted as saying that "you can't manage what you can't measure."
Drucker means that you can't know whether or not you are successful unless success is defined and tracked.
Almost 20 years ago, I was starting to work in a project to do a tool for SPC, I readed that Cpk is meaningless without stability and Wheeler in his book "advanced topics on SPC" said even that other indicators like ppk should not be used because the same condition. I also readed in an article wroted by the most recognized SPC and precontrol practitioners that even with data "fabricated" there will be still some lack of stability.
Well, ok..., so what can I report to get track of the improvement?, is better not to get track of that?
I also readed a very good article about the confidence intervals for capability indexes that showed the meaningless of calculate capability indexes without reporting sample sizes, normaly not taked in account or at least the minimum value (most of us don't like to report the smaller value).
What can make your index more stable numerically (without improvement)?, just larger sample sizes, because it takes all variation sources in account, or normalizate the data (some years ago I did a study with a sample that gave me a mean very different with 200 than with 10000 units, I used normalization methods and with the first 200 gave to me the same as the one with the bigger sample.
:truce:But If you want to convince your management, you can:
* show a book of an authority on the field "Advanced Topics in Statistical Process Control" by Donald J. Wheeler, page 197" by example
* You can show books with the formula and tell them that it take in account the mean and variation estimates, and without normality (and stability affects normality) such parameters theorically nonesensical desto the resulting formulae (capability index) the same.