IESAFE is a good way to make safe choices about parameter settings. Sometimes it is not a disaster to produce less than expected, but there is a certain threshold below which the process must be shut down and restarted. Suppose that the cost of a shut down is 10.0. Then we would like to choose an action that explicitly considers this cost and the probability of incurring it. EMAX can be used for this purpose. First, update the Taskspec to indicate the addition to the cost function:
Optex -> Edit -> Taskspec -> Extra expression: if (yield<0.0) then -10 else 0
Choose
We could use PMAX to choose an action while considering this extra cost. However, PMAX will still choose 0.50. That's because the predicted output for temperature 0.50 will not incur the penalty. PMAX does not consider the fact that the confidence intervals are wide and the actual output may incur the penalty. In contrast, EMAX looks over the whole range of possible outputs and considers the cost of each one as well as the probability of getting it. Therefore, EMAX selects temperature 0.60 because it has a high expected yield and a low probability of incurring the penalty of 10.0. The experiment value function shown in fig. 30c shows how the probability of a yield below 0.0 drastically lowers the value of parameters settings where the confidence intervals reach below 0.0.