Yes, I would post the data for review. 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. You indicated your tolerance was -0.2mm. Did you mean +/- 0.2 or +0.0/-0.2? For +/- 0.2 is a 400 micron (0.4 mm) tolerance. Just to measure the dimension, you should have 10:1 tolerance, or a gage that measures 40 micron increments (.04 mm). For SPC, you should be within 75% of your tolerance, so the gage should be even closer to 30 micron increments. You need this resolution to accurately flesh out the distribution. 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. For example, if you were doing precision machining, for example, the expected distribution is non-normal due to tool wear, and if you passed normality tests it would actually be a bad thing - usually excessive gage or measurement error masking the true distribution. Do you know what your true expected distribution should be? Rather than blindly doing a normality test, I prefer curve fitting, such as Distribution Analyzer from variation.com, to see if it is non-normal, and if so what distribution is a better model of the process variation.