The following situation has been considered: during an accident sequence, a crew has to do a proper set of actions within a finite time window in order to achieve a specific goal. The operator actions are considered independent, they are lined up in series, and a single failure leads to mission failure. This paper proposes a general methodology for assessing the crew response (or success) probability, through a convolution integral formulation. This method is general and can be applied to any response probability model; an application to the Human Cognitive Reliability model is given.