I am suspicious as to what you indicated that your gage has way too little resolution for SPC. If you did a gage R&R, you need an ndc of about 10. I do not think that is possible with your spec and that gage. ... Chunky data from insufficient resolution will not calculate the distribution correctly. I think you find that with the correct resolution, the correct measurement technique - and if the expected distribution is normal - your data will be normal.