Finding limits of multiple vision inspections for one SOP quality

[#1]

I have a situation where i have some operators rating a object which I am fitting my vision system accordingly too. The result of this should be the trained vision system places reject products in a reject box and accept products in accept box. Due to these products are hard to rate the it is okay to have accepted products in a reject box but not vice versa, of cause we try to limit this.

In this example my operators rate one specific quality category named Y1 where my vision system have six different inspections to numeric score Y1, see image below:

The standard have been to look at the data and then narrow the limits as shown in the image until no reject products are in accept box but i think it we can do it smarter.

If the vision system only had one inspection then I would create a ROC Curve to find a limit but i have no experience when it is multi dimensional and i have a hard time to figure out how to do this smart in jmp. If you also have a idea how to do this illustrative then please enlighten me. I have attached an anomynized data set.

Best regards Søren 

[#2 · Accepted solution]

You should use fit model to built a multi dimmensional logistics model and optimize that for your false postive/negative rate.

[#3]

Thank you very much for the elegant answer.

Have you any ideas if i had a upper and a lower spec ?

[#4]

What about spec limits? You need to define that based on the model you build and its balance between false and true classification rates.