2-sample t-test shows no equal means, can I still compare capabilty analysis and Ppk's?

I want to compare two categorical situations (old vs. new part in a machine) with the continuous CTQ, the y-variable.

In order to compare the 2 situations, I found the proper distribution and compared the two Ppk values. I saw a significant difference in performance (the new part was +-3 times better in terms of exceeding the USL and LSL).

However, I also performed a 2-sample t-test and test for equal variance. Both of these ‘failed’ and showed no significant difference in either the mean or variance between the population of the new part and the old part. I also performed a power & sample size test to ensure I had enough data points in my samples/populations.

Can I still use the difference between the capability analysis as evidence of the new part significantly outperforming the old part, or is this not possible since there is no significant difference between the mean and variance?

Thanks in advance!