It would be useful to have the capability not to update one of the limits. Not every parameter can be modeled as a normal random variable, so you might want to consider letting the users specify how to approximate the distribution of each parameter. Of course, there are many different types of random variables, but the inclusion of a few choices would help in evaluating the risk for some situations. You can use the normal random variable to model results of tester experiments. Its probability density function is shown here.
Every measurement has an associated uncertainty.
It is also important for product yield, because a conservative guardband will result in the ATE rejecting good parts. To determine how uncertain each measurement is, you can model each test parameter as a random variable. It remains to determine s from actual data. Use a minimum of 30 units over at least four configurations. For quad-site testing, you can use all four sites on one DUT board.