While I agree with characterisation sometimes, it is often vital to know the transfer function in advance, and monitor the deviation of that from the model rather than assume you can model out discrepanicies. In one of my instruments, with a torque sensor based on an LVDT, we calibrate at 7 fixed points on a straight line and use the correlation coefficient as a measure of quality. We have to achieve 0.9997 before the calibration is acceptable. We usually achieve 0.9999 or 0.99999.

One of our customers assumed that the model was correct, and that he could use only three points, because that is one more than you need to fit a straight line. Unfortunately the real transfer function looked like this.

Steve