PID Control

A PID controller is a control loop feedback mechanism commonly used in industrial applications. – PID Controller, Wikipedia

Area under the Curve (AUC)

The idea that the area under the temperature curve could be an indicator on how much total energy the beans might have receive during the roasting process popped up already some years ago. While the rate-of-rise (RoR) of a temperature curve, calculated as the first (discrete) derivation, gives the current "speed" of the temperature increase and allows to predict the future, the area-under-the-curve (AUC) describes the past.