I'm shocked that
@Bev D didn't mention this, but technically speaking, you can't prove that the possibility of particular defect has been eliminated. (Unless of course you eliminate the part/component on which the defect materializes, or you change your process to eliminate
all causes of the defect). Statistically, you can only demonstrate that the likelihood of the defect has been reduced to a certain amount. That amount may be 1 in a thousand, 1 in 10k, or even 1 in 1 million. Your test sampling plan will dictate the AQL/reliability and confidence level you can claim.
So all of that goes to say, I think
@William55401 and Bev provided great advice. You should have a pre-determined effectiveness acceptance criteria. If you have sufficient historical data, you can probably justify (and demonstrate) a return to, or improvement beyond, the original defect rate. If you don't have that historical data, and/or you haven't defined a certain reliability/confidence level as being acceptable, then you may just have to present your post-improvement data, and have a cross-functional decision made regarding the effectiveness of actions. That decision should be based on risk and some established precedent. For example, ISO 14971 requires manufacturers to (1) establish a policy for determining acceptable risk, and (2) document criteria for the acceptability of both individual risks and overall residual risk. You can should be able to draw some conclusion based on those.