Nice, thanks for sharing! Typically, TAN is used in transmission fluids as such: obtain the virgin TAN, then take a used sample of the same fluid later. The value will increase with use. What I've read is that once the used value is 3x-4x higher than the virgin value, then the fluid is spent. I've also read that it can be used in conjunction with TBN on engine oil and where the two cross over is the indication that the oil is spent. So let's say TBN starts at 7.61 and TAN starts at 1.94. At some point during use, TAN will become the larger number. When that happens, the oil is considered spent. I don't know how valid the second method is, I've heard it is outdated now. But just relaying what I've read.
It's critical is using TAN that you have the starting virgin value because some fluids have a much higher starting TAN than others. Let's say you're testing transmission fluid. You're using one type/brand to obtain the virgin value and another type/brand in your transmission. If the virgin TAN of one type/brand is 4 but the other is 1.5, then you can see how it would be easy to condemn a good fluid or keep using a spent fluid.
edit: and this is why you can get information from used TBN without having the virgin value. Because TBN becomes condemned when it reaches a low point (some say 2, other say 1). You don't need the starting value, just the ending value. But a used TAN is useless without also having the starting value of the same fluid.