I would start with one type of problem, such as returns of a given part number for a given issue. add up how many times it has happened in a period.
Add the cost of personnel time, equipment and/or materials and whatever else is specifically consumed to make it right with the issue. This would be the cost of one event. It might vary from one occurrence to the next, try not to fixate on that and come up with an average. The point is to quantify COPQ.
Next, quantify the cost of fixing the issue causing the given issue. personnel time, equipment and/or materials, etc.
After the change is made, compare the number of this particular issue's occurrence for the same period as originally counted. If the number of orders is different, you can calculate your data into ratios in order to normalize the frequency.
The cost improvement is the difference between the original frequency data and the frequency following the improvement.
Two important points:
1) Target a specific issue type instead of a range of issues and responding actions. You want to know that the effect was as desired and attributable to these specific actions.
2) Trending is more important than trying to count every dime.
If you don't feel you have time for all the above targeted study steps, you can add it up overall but unless you made a single type of process change you might not know just what it was that made the difference.