Interpretation & Calculations
I am not sure whether I should use a normal or non-normal curve fit for calculating process capability. I have tried both, and compare the K-S statistic, but both K-S are small.
Part of the problem you have with fitting curves (normal or non-normal) is that your data is out of control. An extremely small K-S (less than 0.05) is an indication that the data is not well fit by the chosen distribution. If the process is out of control, then by definition there are multiple distributions, so it stands to reason that one given distribution may not fit well. I say may not since you can get software to fit a good distribution, even a normal distribution, when the process is out of control, if the data just so happens to look not so different than the assumed distribution. So a bad fit may reflect out of control or wrong distribution, and a good fit can still occur if the process is out of control. Technically, a good fit may also occur even when the wrong distribution is chosen, but so long as it works for us in predicting the process, then that is good enough. (George Box said it as: All models are wrong, but some are useful).
Start by verifying the process is in control, then worry about capability analysis and curve fitting. See Process Capability for Non-Normal Data Cp, Cpk
Learn more about the SPC principles and tools for process improvement in Statistical Process Control Demystified (2011, McGraw-Hill) by Paul Keller, in his online SPC Concepts short course (only $39), or his online SPC certification course ($350) or online Green Belt certification course ($499).