In addition to the three characteristic quantities, which are defined per vial, the process duration is a quantity of key interest. We define the process duration as the time of complete nucleation for a batch t nuc c , i.e., the duration from beginning of the cooling process until the nucleation of the last vial. This time will inherently vary due to the stochasticity of ice nucleation, and the process needs to be designed in a way that ensures that all vials are eventually frozen with sufficiently high probability.