Hi @KarlA026 : Yes, that is helpful. Thanks!
The idea, as I understand it, is to build a probabilistic model that is based on the data in the figure. That model can then be used to estimate the probability of that sample coming from each of the suppliers, respectively (based on the observed value of material property X).
Case 1 (material from unknown supplier): You measure X. Then once you have the observed value of X, just apply to model you've already built (logistic/ANN/whatever) to predict the most likely supplier (supplier with highest probability).
Case 2 (material from known supplier): If you know the supplier and you know X, the probability of this material being from that supplier (or, not) is irrelevant (though it can be calculated, same as in case 1 above). Here is an example. Let's suppose you look outside and it is raining. But, an hour ago you checked the weather forecast and it said, then, that the probability of rain today is 10%. All you can really say, from a binary prediction point of view, is that the model got it wrong; from a probabilistic view, however, the model wasn't wrong (it didn't say the chance of rain was 0%). But, either way, it's raining...probability doesn't enter into it. So, once something has occurred or is known, there can be no probability associated with it. In your case, once you know the supplier, there can be no probability associated with it...though you can calculate it (just as in case 1 above) to see how well the model predicts. So, if the model predicts supplier M, but you know it actually came from supplier F...all you can say, from a prediction point of view, is that the model got it wrong. That said, do you have some reason to distrust a supplier? e.g., is there a chance you get a sample from supplier D that is actually from supplier B? If so, that is a different situation, with an easy solution (don't use supplier D anymore!).
